IUC AcademyHome81. N solid metallic spherical balls are melted an d recast into a cylindrical rod whose radius is 3 times that of a spherical ball and height is 4 times the radius of a spherical ball. The value of N is
- A. 30
- B. 27
- C. 24
- D. 36
Answer: 27
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82. A right circular cylinder has height 28 cm and radius of base 14 cm. Two hemispheres of radius 7 cm each are cut from each of the two bases of the cylinder. What is the total surface area (in cm2) of the remaining part ?
- A. 3842
- B. 4312
- C. 3296
- D. 4436
Answer: 4312
Explanation: Radius of cylinder (R) = 14 cm (h) = 28 Radius of hemisphere (r) = 7cm Area of upper and lower surface after cutting the hemisphere = 2πR2 - 4πr2 = 2 π (R2 - 2r2) = 2 π( 14 × 14 - 2 × 7 × 7 ) = 222 987× × = 616 cm 2 Area of curved surface of cylinder = 2 πr2 + 2 πr2 + 2πr2 + 2πr2 = 8πr2 = 228 7 77× × × = 1232 cm 2 Area of curved surface of cylinder = 2 πRh = 222 14 287× × × = 2464 cm2 According to the question Surface area of remains part = 616 + 1232 + 2464 = 4312cm 2
Explanation: Radius of cylinder (R) = 14 cm (h) = 28 Radius of hemisphere (r) = 7cm Area of upper and lower surface after cutting the hemisphere = 2πR2 - 4πr2 = 2 π (R2 - 2r2) = 2 π( 14 × 14 - 2 × 7 × 7 ) = 222 987× × = 616 cm 2 Area of curved surface of cylinder = 2 πr2 + 2 πr2 + 2πr2 + 2πr2 = 8πr2 = 228 7 77× × × = 1232 cm 2 Area of curved surface of cylinder = 2 πRh = 222 14 287× × × = 2464 cm2 According to the question Surface area of remains part = 616 + 1232 + 2464 = 4312cm 2
83. A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder ?
- A. 5
- B. 6
- C. 15
- D. 7.5
Answer: 7.5
Explanation: Radius of second cylinder (R) ⇒ R2 = (6)2 + (4.5)2 R 2 = 36 + 20.25 R = 7.5cm
Explanation: Radius of second cylinder (R) ⇒ R2 = (6)2 + (4.5)2 R 2 = 36 + 20.25 R = 7.5cm
84. The radius and height of a solid cylinder are increased by 2% each. What will be the approximate percentage increase in volume?
- A. 6.76
- B. 5.88
- C. 6.12
- D. 3.34
Answer: 6.12
85. A right circular cylinder is formed A = sum of total surface area and the area of the two bases. B = the curved surface area of this cylinder. If A : B = 3 : 2 and the volume of cylinder is 4312 cm3, then what is the sum of area (in cm 2) of the two bases of this cylinder ?
- A. 154
- B. 308
- C. 462
- D. 616
Answer: 308
86. A cylindrical road roller made of metal is one meter. Its inner radius is 27 cm and the thickness of the metal sheet rolled into it is 9 cm. What is the weight of the roller if 1 cm 3 of the metal weight 8g?
- A. 442.4 kgπ
- B. 449 kgπ
- C. 453.6 kgπ
- D. 441 kgπ
Answer: 453.6 kgπ
87. The radii of two cylinders are in the ratio 3 :4 and their heights are in the ratio 8 : 5. The ratio of their volumes is equal to
- A. 9 : 10
- B. 8 : 9
- C. 9 : 11
- D. 7 : 10
Answer: 9 : 10
88. The curved surface area of a cylinder is five times the area of its base. Find the ratio of radius and height of the cylinder.
- A. 3 : 5
- B. 2 : 5
- C. 2 : 3
- D. 3 : 4
Answer: 2 : 5
Explanation: Let, The radius and height of cylinder is r and h respectively Curved surface area of cylinder 2 rh= π Area of base of cylinder = 2rπ According to the question C.S.A. = 5 × area of its base 2 πrh = 5 [πr2] 2 πrh = 5πr2 2h = 5r r 2h 5= Hence, The ratio of radius and height of cylinder = 2:5
Explanation: Let, The radius and height of cylinder is r and h respectively Curved surface area of cylinder 2 rh= π Area of base of cylinder = 2rπ According to the question C.S.A. = 5 × area of its base 2 πrh = 5 [πr2] 2 πrh = 5πr2 2h = 5r r 2h 5= Hence, The ratio of radius and height of cylinder = 2:5
89. A solid metallic right circular cylinder has diameter 32 cm and height 9 cm. It is melted and recast into a solid sphere. What is the radius (in cm) of the sphere?
- A. 14
- B. 25
- C. 12
- D. 10
Answer: 12
Explanation: ∵ Solid metallic circular cylinder is melted and recast into a solid sphere. ∴ Volume of sphere = Volume of right circular cylinder 43 πR3 = πr2h 43 R3 = 16×16×9 R 3 = 64×27 R = 12 cm
Explanation: ∵ Solid metallic circular cylinder is melted and recast into a solid sphere. ∴ Volume of sphere = Volume of right circular cylinder 43 πR3 = πr2h 43 R3 = 16×16×9 R 3 = 64×27 R = 12 cm
90. If the ratio of the curved surface area and volume of a right circular cylinder is 5:7, then its radius is
- A. 2.6 units
- B. 3.8 units
- C. 3.2 units
- D. 2.8 units
Answer: 2.8 units
Explanation: Given, Curved surface area of the cylinderVolume of the cylinder = 57 ⇒ 22 rh 5 7r hπ =π 2×7 = 5r r = 145 = 2.8 units
Explanation: Given, Curved surface area of the cylinderVolume of the cylinder = 57 ⇒ 22 rh 5 7r hπ =π 2×7 = 5r r = 145 = 2.8 units
91. Two similar jugs have their heights of 8 cm a nd 12 cm, respectively. If the capacity of the smaller jug is 80 cm 3, what is the capacity of the bigger jug (in cm3)?
- A. 120
- B. 192
- C. 216
- D. 270
Answer: 270
92. Find the volume of a cylinder whose diameter of base is 20 cm and height is two times that of the radius of its base.
- A. 4000 cm3
- B. 2000π cm3
- C. 6000π cm3
- D. 3000 cm3
Answer: 2000π cm3
Explanation: Radius of cylinder = 10 cm Height of cylinder = 20 cm Volume of cylinder = πr2h = π(10)2 × 20 = 2000 π cm3
Explanation: Radius of cylinder = 10 cm Height of cylinder = 20 cm Volume of cylinder = πr2h = π(10)2 × 20 = 2000 π cm3
93. The sum of the radius of the base and height of a solid cylinder is 17 cm. If the total surface area of a solid cylinder is 748 cm 2, Find the height of the cylinder.
- A. 10 cm
- B. 15 cm
- C. 12 cm
- D. 14 cm
Answer: 10 cm
Explanation: According to the question, r + h = 17 ______(i) Total surface area of cylinder = 748 cm 2 2 πr (h + r) = 748 222 r 17 7487× × × = 748 7r 7cm2 22 17×= =× × From equation (i) 7 + h= 17 h = 17 - 7 ⇒ h = 10 cm
Explanation: According to the question, r + h = 17 ______(i) Total surface area of cylinder = 748 cm 2 2 πr (h + r) = 748 222 r 17 7487× × × = 748 7r 7cm2 22 17×= =× × From equation (i) 7 + h= 17 h = 17 - 7 ⇒ h = 10 cm
94. The total surface area of a cylinder is 4092 cm 2 and the diameter of its base is 21cm. What will be 50% of the volume of the cylinder (in cm 3) rounded to the nearest integer) ?
- A. 8922
- B. 8932
- C. 8822
- D. 8832
Answer: 8922
95. The radius of the base of a cylindrical, tank is 4m. If three times the sum of the areas of its two circular faces is twice the area of its curved surface, then the capacity (in Kilolitres) of the tank is
- A. 108 π
- B. 144 π
- C. 54 π
- D. 96 π
Answer: 96 π
96. A cylindrical vessel of diameter 32 cm is partially filled with water. A solid metallic Sphere of radius 12 cm is dropped into it . What will be the increase in the level of water in the vessel (in cm).
- A. 2.25
- B. 27
- C. 72
- D. 9
Answer: 9
97. The ratio of heights of two cylinder is 1 : 2 and the ratio of their radii is 2 : 1. What will be the ratio f their volumes?
- A. 3 : 1
- B. 2 : 1
- C. 1 : 2
- D. 1 : 3
Answer: 2 : 1
98. A hemispherical bowl of internal radius 18cm filled with liquid. This liquid is to be filled int o cylindrical bottles of radius 3cm and height 6 cm. What is the number of bottles used to empty the bowl?
- A. 68
- B. 72
- C. 66
- D. 70
Answer: 72
99. What will be the volume of the cylinder if its radius is 10 cm and height is 20 cm?
- A. 6260 cm3
- B. 6280 cm3
- C. 5306 cm3
- D. 5280 cm3
Answer: 6280 cm3
100. The external diameter of an iron pipe is 20cm and its length is 12cm. If the thickness of the pipe is 1cm, find the total surface area of the pipe (take 227π =π = π =π = ) correct to two places of decimal.
- A. 1,662.67 cm2
- B. 1,772.76 cm2
- C. 1,552.57 cm2
- D. 1,442.48 cm2
Answer: 1,552.57 cm2
Explanation: External radius of the iron pipe (R) = 10 cm Height (h) = 12 cm Internal radius of the iron pipe (r) = 10 - 1 = 9 cm ง Total surface area of the pipe = Curved surface ar ea of pipe + Area of both base 2 22 (R r)h 2 (R r )= π + + π - 2 (R r)[h R r]= π + + - [ ]222 19 12 17= × × × + = 1552.57 cm 2
Explanation: External radius of the iron pipe (R) = 10 cm Height (h) = 12 cm Internal radius of the iron pipe (r) = 10 - 1 = 9 cm ง Total surface area of the pipe = Curved surface ar ea of pipe + Area of both base 2 22 (R r)h 2 (R r )= π + + π - 2 (R r)[h R r]= π + + - [ ]222 19 12 17= × × × + = 1552.57 cm 2
101. If the numerical value of the twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then find the numerical value of the radius of the base of the cylinder.
- A. 2
- B. 3
- C. 4
- D. 5
Answer: 4
Explanation: Curved surface area of right circular cylinder = 2πrh Volume of right circular cylinder = πr2h 2(2πrh) = πr2h 4πrh = πr2h 4r = r2 ง r 4=
Explanation: Curved surface area of right circular cylinder = 2πrh Volume of right circular cylinder = πr2h 2(2πrh) = πr2h 4πrh = πr2h 4r = r2 ง r 4=
102. The radii of two cylinders are in the ratio 2 : 1 and their heights are 5: 2 . The ratio of their volumes is .
- A. 5 : 1
- B. 10 : 1
- C. 15 : 1
- D. 20 : 1
Answer: 10 : 1
103. A toy is in the shape of a cylinder surmounted by a hemisphere. The total height of the toy is 15cm and the radius of the hemisphere is 6 cm . Find the volume of the toy.
- A. 476π cm3
- B. 458π cm3
- C. 496π cm3
- D. 468π cm3
Answer: 468π cm3
Explanation: According to the question, h = 15 - r = 15 - 6 = 9 cm ง Volume of the toy = Volume of semicircle + volume of cylinder = 3 22 r r h3 π + π = 32 (6) 36 93 π + π× × = 144 π + 324 π = 468 π cm3
Explanation: According to the question, h = 15 - r = 15 - 6 = 9 cm ง Volume of the toy = Volume of semicircle + volume of cylinder = 3 22 r r h3 π + π = 32 (6) 36 93 π + π× × = 144 π + 324 π = 468 π cm3
104. A right prism has height 18 cm and its base is a triangle with sides 5 cm, 8 cm and 12 cm. What is its lateral surface area (in cm 2)?
- A. 432
- B. 450
- C. 486
- D. 468
Answer: 450
Explanation: Lateral surface area of the prism = Perimeter of the base × Height = (5+8+12) × 18 = 25 × 18 = 450 cm2
Explanation: Lateral surface area of the prism = Perimeter of the base × Height = (5+8+12) × 18 = 25 × 18 = 450 cm2
105. A petrol tank is of length 50m, breadth 25m, and depth 10m. How many litres of petrol can be accommodated in the petrol tank when it is completely filled?
- A. 12,50,000 Litre
- B. 1,25,000 Litre
- C. 12500 Litre
- D. 1,25,00,000 Litre
Answer: 1,25,00,000 Litre
106. The length, breadth and height of a solid cuboid is 14 cm, 12 cm and 8 cm respectively. If cuboid is melted in form of identical cubes of side 2 cm, then what will be the number of identical cubes?
- A. 168
- B. 144
- C. 156
- D. 128
Answer: 168
107. The area of the sheet metal needed to make a box of size 7 cm × 8 cm × 9 cm is
- A. 382 cm2
- B. 156 cm2
- C. 412 cm2
- D. 139 cm2
Answer: 382 cm2
Explanation: Area of required sheet metal = 2(lb+bh+hl) = 2(7×8 + 8×9 + 9×7) = 2(56 + 72 + 63) = 2×191 = 382 cm 2
Explanation: Area of required sheet metal = 2(lb+bh+hl) = 2(7×8 + 8×9 + 9×7) = 2(56 + 72 + 63) = 2×191 = 382 cm 2
108. The length, breadth and height of a cuboid are 18cm, 24cm and 4cm respectively. The volume of cube is equal to the volume of given cuboid. The side of the cube is
- A. 9 cm
- B. 16 cm
- C. 12 cm
- D. 8 cm
Answer: 12 cm
Explanation: Let side of cube is a. Volume of cuboid =Volume of cube 18 × 24 × 4 = a3 a3 = 1728 a = 12cm
Explanation: Let side of cube is a. Volume of cuboid =Volume of cube 18 × 24 × 4 = a3 a3 = 1728 a = 12cm
109. A cuboidal tank has 25000 litres of water. If t he depth of the cuboid is 1/5 of its length and breadth is 1/8 of its length, then the length of the tank is
- A. 18 m
- B. 12 m
- C. 10 m
- D. 15 m
Answer: 10 m
110. If a cuboid of dimensions 32 cm × 12 cm × 9 cm is cut into two cubes of same size, what will be the ratio of the surface area of the cuboid to the total surface area of the two cubes ?
- A. 32 : 39
- B. 24 : 35
- C. 37 : 48
- D. 65 : 72
Answer: 65 : 72
111. The base of a right prism is a square having side of 15 cm. If its height is 8 cm, then find the total surface area.
- A. 900 cm 2
- B. 920 cm 2
- C. 940 cm 2
- D. 930 cm 2
Answer: 930 cm 2
Explanation: Total surface area = Perimeter× Height + 2 × Area of base = 4 × 15 × 8 + 2 × 152 = 60 × 8 + 2 × 225 = 480 + 450 = 930 cm 2
Explanation: Total surface area = Perimeter× Height + 2 × Area of base = 4 × 15 × 8 + 2 × 152 = 60 × 8 + 2 × 225 = 480 + 450 = 930 cm 2
112. A solid cuboid has dimensions 14 cm × 18 cm × 24 cm. A hemisphere of radius 3.5 cm is cut from the centre of each face of cuboid. What is the total surface area (in cm2) of the remaining solid ?
- A. 1902
- B. 1809
- C. 1706
- D. 2271
Answer: 2271
113. A cuboid has dimensions 8 cm × 10 cm × 12 cm. It is cut into small cubes of side 2 cm. What is the percentage increase in the total surface area ?
- A. 286.2
- B. 314.32
- C. 250.64
- D. 386.5
Answer: 386.5
114. The length, breadth and height of a cuboidal box are in the ratio 7 : 5 : 3 and its whole surface area is 27832 cm2. Its volume is
- A. 208120 cm 3
- B. 280120 cm 3
- C. 288100 cm 3
- D. 288120 cm 3
Answer: 288120 cm 3
115. The area of the four walls of a room having length 6m, breadth 4m and height 4m, is
- A. 50
- B. 60
- C. 40
- D. 80
Answer: 80
116. The areas of the three adjacent faces of a cuboid are 32 cm 2, 24 cm 2 and 48 cm 2. What is the volume of the cuboid?
- A. 192 cm 3
- B. 288 cm 3
- C. 128 cm 3
- D. 256 cm 3
Answer: 192 cm 3
117. The sum of length, breadth and height of a cuboid is 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of cuboid.
- A. 356 cm 2
- B. 364 cm 2
- C. 256 cm 2
- D. 264 cm 2
Answer: 256 cm 2
Explanation: According to the question l + b + h = 20 ______ (1) Diagonal = 12 cm Hence, Diagonal = 2 2 2b h+ +l = 12 On squaring both side = l2 + b2 + h2 = 144 ___ (2) ∵ (l+b+h)2 = l2 + b2 + h2 + 2(lb+bh+hl) (20)2 = 144 + 2(lb+bh+hl) 2(lb+bh+hl) = 256 cm2
Explanation: According to the question l + b + h = 20 ______ (1) Diagonal = 12 cm Hence, Diagonal = 2 2 2b h+ +l = 12 On squaring both side = l2 + b2 + h2 = 144 ___ (2) ∵ (l+b+h)2 = l2 + b2 + h2 + 2(lb+bh+hl) (20)2 = 144 + 2(lb+bh+hl) 2(lb+bh+hl) = 256 cm2
118. The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm 2, 96cm 2 and 144 cm2. It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm2) of 3 such cubes?
- A. 648
- B. 432
- C. 576
- D. 288
Answer: 648
119. What is the length (in cm) of the longest rod that can be fitted in a box of dimensions 28 cm × 4 cm × 10 cm?
- A. 36
- B. 42
- C. 25
- D. 30
Answer: 36
120. The length of the longest pole that can be fitted in a room of dimensions 12 m × 6 m × 4 m is: (in m, correct to one decimal place)
- A. 7.2
- B. 14.0
- C. 13.4
- D. 12.6
Answer: 14.0
121. The sum of the length, breadth and height of a cuboid is 28 cm. If the total surface area of the cuboid is 588 cm2, then its diagonal is
- A. 14 cm
- B. 12 cm
- C. 16 cm
- D. 15 cm
Answer: 14 cm
Explanation: Let, length = l, breadth = b and height = h Given, l + b + h = 28 ...........(i) Total surface area of cuboid ⇒ 2(lb + bh + hl) = 588......(ii) Diagonal of cuboid, 2 2 2b h ?= + + =l From equation (i), l + b + h = 28 On squaring both sides, ( l + b + h)2 = (28)2 l2 + b2 + h2 + 2 (lb + bh + hl) = 784 Putting value of equation (ii), l2 + b2 + h2 + 588 = 784 l2 + b2 + h2 = 784 - 588 l2 + b2 + h2 = 196 2 2 2b h 196+ + =l 2 2 2b h 14+ + =l Hence, diagonal of cuboid = 14 cm
Explanation: Let, length = l, breadth = b and height = h Given, l + b + h = 28 ...........(i) Total surface area of cuboid ⇒ 2(lb + bh + hl) = 588......(ii) Diagonal of cuboid, 2 2 2b h ?= + + =l From equation (i), l + b + h = 28 On squaring both sides, ( l + b + h)2 = (28)2 l2 + b2 + h2 + 2 (lb + bh + hl) = 784 Putting value of equation (ii), l2 + b2 + h2 + 588 = 784 l2 + b2 + h2 = 784 - 588 l2 + b2 + h2 = 196 2 2 2b h 196+ + =l 2 2 2b h 14+ + =l Hence, diagonal of cuboid = 14 cm
122. From a rectangle sheet of dimensions 32 cm × 18 cm, a square of side 3 cm is cut from the four corners of the sheet and a box is made. The volume of the box is
- A. 946 cm3
- B. 1300 cm3
- C. 936 cm3
- D. 1305 cm3
Answer: 936 cm3
Explanation: If square of side 3cm is cut off from corners then height of box = 3 cm Length of box = 32 - (3 + 3) = 26 cm Breadth of box = 18 - (3 + 3) = 12cm Hence, the volume of the box = 26 × 12 × 3 = 936 cm 3
Explanation: If square of side 3cm is cut off from corners then height of box = 3 cm Length of box = 32 - (3 + 3) = 26 cm Breadth of box = 18 - (3 + 3) = 12cm Hence, the volume of the box = 26 × 12 × 3 = 936 cm 3
123. Four cubes, each of edge 5 cm are joined end to end. What is the total surface area of the resulting cuboid?
- A. 450 cm2
- B. 500 cm2
- C. 475 cm2
- D. 600 cm2
Answer: 450 cm2
Explanation: Length of cuboid made by joining 4 cube of 5cm core = 5 × 4 = 20 cm Breadth = 5 cm, Height = 5 cm Total surface area of cuboid = 2 (l×b+b×h+h×l) = 2 (20 × 5 + 5 × 5 + 5 × 20) = 2 × (100 + 25 +100) = 2 × 225 = 450 cm 2
Explanation: Length of cuboid made by joining 4 cube of 5cm core = 5 × 4 = 20 cm Breadth = 5 cm, Height = 5 cm Total surface area of cuboid = 2 (l×b+b×h+h×l) = 2 (20 × 5 + 5 × 5 + 5 × 20) = 2 × (100 + 25 +100) = 2 × 225 = 450 cm 2
124. The area of a cardboard (in cm 2) needed to make a closed box of size 20 cm × 10 cm × 8 cm will be
- A. 880
- B. 690
- C. 750
- D. 960
Answer: 880
Explanation: Given that- Length of box (l) = 20cm Breadth of box (b) = 10cm Height of box (h) = 8cm According to the question, Area of cardboard = Total surface area of box = 2 (lb + bh + lh) = 2(20 × 10 + 10 × 8 + 20 × 8) = 2(200 + 80 + 160) = 2 × 440 = 880 cm2
Explanation: Given that- Length of box (l) = 20cm Breadth of box (b) = 10cm Height of box (h) = 8cm According to the question, Area of cardboard = Total surface area of box = 2 (lb + bh + lh) = 2(20 × 10 + 10 × 8 + 20 × 8) = 2(200 + 80 + 160) = 2 × 440 = 880 cm2
125. If the length of a cuboid is 20 m, breadth is 5 m and height is 4 m, then find the length of diagonal of the cuboid.
- A. 12 m
- B. 21 m
- C. 18 m
- D. 24 m
Answer: 21 m
126. Find the total surface area of a cuboid whose length, breadth, and height are 20 cm. If the length of the diagonal is 12 cm, then find the total surface area of cuboid.
- A. 356 cm 2
- B. 364 cm 2
- C. 256 cm 2
- D. 264 cm 2
Answer: 256 cm 2
Explanation: According to the question l + b + h = 20 ______ (1) Diagonal = 12 cm Diagonal = 2 2 2b h+ +l = 12 = l2 + b2 + h2 = 144 ___ (2) ∵ (l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl) (20)2 = 144 + 2(lb + bh + hl) 2(lb + bh + hl) = 256 cm2
Explanation: According to the question l + b + h = 20 ______ (1) Diagonal = 12 cm Diagonal = 2 2 2b h+ +l = 12 = l2 + b2 + h2 = 144 ___ (2) ∵ (l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl) (20)2 = 144 + 2(lb + bh + hl) 2(lb + bh + hl) = 256 cm2
127. Find the total surface area of a cuboid whose length ,breadth, and height are 20cm, 15cm and 8 cm respectively.
- A. 990 cm 2
- B. 1120 cm 2
- C. 1160 cm 2
- D. 1080 cm 2
Answer: 1160 cm 2
Explanation: Total surface of area of cuboid = 2 (l ² b ± b ² h ± h ² l) = 2 (20 × 15 + 15 × 8 + 8 × 20) = 2 (300 + 120 + 160) = 2 × 580 = 1160 cm 2 Hence, total surface area of cuboid is 1160 cm 2
Explanation: Total surface of area of cuboid = 2 (l ² b ± b ² h ± h ² l) = 2 (20 × 15 + 15 × 8 + 8 × 20) = 2 (300 + 120 + 160) = 2 × 580 = 1160 cm 2 Hence, total surface area of cuboid is 1160 cm 2
128. If the length breadth and height of a cuboid are 20m, 5m and 4 m respectively, then find the length of the diagonal of the cuboid.
- A. 12 m
- B. 24 m
- C. 21 m
- D. 18 m
Answer: 21 m
129. The measures of the outer sides of a closed metal box are given as 15 cm ×18cm ×8cm. The thickness of the metal is 1.5cm. What will be the volume of the metal required to make the box.
- A. 1260 cm3
- B. 950 cm3
- C. 1680 cm3
- D. 1440 cm3
Answer: 1260 cm3
Explanation: Volume of metal = External volume - Internal volume External volume of box = (15 ×18 ×8) = 2160 cm 3 Internal measurement ⇒ l = 15 - 1.5 × 2 = 12 b = 18 - 1.5 × 2 = 15 h = 8 - 1.5 × 2 = 5 Internal volume of box = 12 × 15 × 5 = 900 cm 3 Hence, Volume of metal required to make the box = 2160 - 900 = 1260 cm3
Explanation: Volume of metal = External volume - Internal volume External volume of box = (15 ×18 ×8) = 2160 cm 3 Internal measurement ⇒ l = 15 - 1.5 × 2 = 12 b = 18 - 1.5 × 2 = 15 h = 8 - 1.5 × 2 = 5 Internal volume of box = 12 × 15 × 5 = 900 cm 3 Hence, Volume of metal required to make the box = 2160 - 900 = 1260 cm3
130. Which of the following two will provide more volume? I) A cuboid of edges 6cm, 7cm, and 8cm II) A cube of edge 7cm
- A. Volume of both will be equal
- B. Cuboid will have more volume
- C. Cube will have more volume
- D. Cannot defined
Answer: Cube will have more volume
131. A cuboid with sides 12cm, 18cm, and 27cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to the total surface area of the cube.
- A. 18 : 17
- B. 17 : 23
- C. 19 : 18
- D. 17 : 19
Answer: 19 : 18
Explanation: According to the question, Volume of cube = Volume of cuboid a3 = lbh a3 = 12×18×27 ง a = 18 cm Now, ง Total surface area of cuboid : Total surface area of cube. 2(lb+bh+lh) : 6a 2 ⇒ 2(12×18+18×27+27×12) : 6 ×(18) 2 ⇒ 2(216+486+324) : 6×18×18 ⇒ 1026 : 3×18×18 ง 19 : 18
Explanation: According to the question, Volume of cube = Volume of cuboid a3 = lbh a3 = 12×18×27 ง a = 18 cm Now, ง Total surface area of cuboid : Total surface area of cube. 2(lb+bh+lh) : 6a 2 ⇒ 2(12×18+18×27+27×12) : 6 ×(18) 2 ⇒ 2(216+486+324) : 6×18×18 ⇒ 1026 : 3×18×18 ง 19 : 18
132. The volume of a cuboid is 3300 cm 3. The sum of length and breadth of the cuboid is 37 cm. If the difference between the length and breadth of the cuboid is 13 cm. Then find the height of the cuboid.
- A. 16 cm
- B. 14 cm
- C. 11 cm
- D. 18 cm
Answer: 11 cm
Explanation: Given that Volume of cuboid = lbh = 3300 cm3 According to the question, l + b = 37 cm …..(i) l - b = 13 cm …..(ii) On adding equation (i) and equation (ii) - 2 l = 50 cm l = 25 cm ∴ b = 12 cm lbh = 3300 cm3 25 cm × 12 cm × h = 3300 cm3 h = 11 cm Hence, the height of the cuboid is 11 cm.
Explanation: Given that Volume of cuboid = lbh = 3300 cm3 According to the question, l + b = 37 cm …..(i) l - b = 13 cm …..(ii) On adding equation (i) and equation (ii) - 2 l = 50 cm l = 25 cm ∴ b = 12 cm lbh = 3300 cm3 25 cm × 12 cm × h = 3300 cm3 h = 11 cm Hence, the height of the cuboid is 11 cm.
133. A cuboid with sides 4, 6 and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square?
- A. 14.42
- B. 12.24
- C. 12.62
- D. 16.62
Answer: 14.42
Explanation: Total surface area of cuboid = 2(lb + bh + hl) = 2(4 × 6 + 6 × 8 + 8 × 4) = 2(24 + 48 + 32) = 208 unit 2 Total surface area of cuboid = Area of square 208 = (Side)2 Side= 14.42 units
Explanation: Total surface area of cuboid = 2(lb + bh + hl) = 2(4 × 6 + 6 × 8 + 8 × 4) = 2(24 + 48 + 32) = 208 unit 2 Total surface area of cuboid = Area of square 208 = (Side)2 Side= 14.42 units
134. The length, breadth and height of a cuboid are in the ratio 6 : 5: 3. If its total surface area is 1800 cm2, then its volume is
- A. 4500
- B. 4650
- C. 4200
- D. 4800
Answer: 4500
Explanation: Let, the length ( l) breadth(b) and height(h) of the cuboid is 6x, 3x and 2x respectively. Total surface area of cuboid = 2 (l b + bh + hl) 2 (18x 2 + 6x2 + 12 x2) = 1800 36x 2 = 900 x 2 = 25 x = 5 Volume of cuboid = 6x 3x 2x = 36x 3 = 36 125 = 4500 cm 3
Explanation: Let, the length ( l) breadth(b) and height(h) of the cuboid is 6x, 3x and 2x respectively. Total surface area of cuboid = 2 (l b + bh + hl) 2 (18x 2 + 6x2 + 12 x2) = 1800 36x 2 = 900 x 2 = 25 x = 5 Volume of cuboid = 6x 3x 2x = 36x 3 = 36 125 = 4500 cm 3
135. 2541 spherical metallic balls are melted to for m a cube each of whose radius is 1cm. The total surface area of cube (in cm 2) in nearest values will be.
- A. 1936
- B. 2904
- C. 2992
- D. 3168
Answer: 2904
136. How many cubes with a side 10 cm can be cut out of a cube having a side of 10 meter?
- A. 10,000
- B. 1,00,00,000
- C. 1,00,000
- D. 10,00,000
Answer: 10,00,000
137. The edge of a cube is 8 cm. What is the total surface area of the cube?
- A. 128 cm2
- B. 256 cm2
- C. 384 cm2
- D. 484 cm2
Answer: 384 cm2
Explanation: QSide of a cube = 8 Then, total surface area of the cube = 6a 2 = 6×(8) 2 = 6 × 64 = 384 cm 2
Explanation: QSide of a cube = 8 Then, total surface area of the cube = 6a 2 = 6×(8) 2 = 6 × 64 = 384 cm 2
138. The total surface area of a cube is 2904 cm 2. What is the volume of this cube ?
- A. 11748 cm 3
- B. 10848 cm 3
- C. 10748 cm 3
- D. 10648 cm 3
Answer: 10648 cm 3
Explanation: Total surface are a of cube = 2904 cm2 26a 2904= 2 2904a 6= 2a 484= a 22= Volume of cube = a3 = 22 × 22 × 22 = 10648 cm3
Explanation: Total surface are a of cube = 2904 cm2 26a 2904= 2 2904a 6= 2a 484= a 22= Volume of cube = a3 = 22 × 22 × 22 = 10648 cm3
139. If the ratio of the volume of two cubes is 64:27, then what is the ratio of their edges?
- A. 4:3
- B. 16:9
- C. 64:27
- D. 4:9
Answer: 4:3
Explanation: Ratio of volume of two cube V1 : V2 = 64:27 Ratio of side of both cube a1 : a2 = 3 3 1 2V : V = 3 364 : 27 = 4:3
Explanation: Ratio of volume of two cube V1 : V2 = 64:27 Ratio of side of both cube a1 : a2 = 3 3 1 2V : V = 3 364 : 27 = 4:3
140. If the diagonal of a cube is 27 cm, then its volume is
- A. 27 cm3
- B. 32 cm3
- C. 30 cm3
- D. 25 cm3
Answer: 27 cm3
Explanation: Diagonal of cube = 3a 27= By squaring the both side 3a2 = 27 a 2 = 9 a = 3 Volume of cube = (a)3 = (3)3 Volume of cube = 27 cm3
Explanation: Diagonal of cube = 3a 27= By squaring the both side 3a2 = 27 a 2 = 9 a = 3 Volume of cube = (a)3 = (3)3 Volume of cube = 27 cm3
141. If each edge of a cube is increased by 10%, the n the percentage increase in its surface area is
- A. 20%
- B. 22%
- C. 19%
- D. 21%
Answer: 21%
142. The volume of a cube is 343 cm 3. The edge of cube is
- A. 7 cm
- B. 6 cm
- C. 5 cm
- D. 4 cm
Answer: 7 cm
Explanation: ∵ Volume of cube = 343 cm3 Let length of side of cube is a then Volume of cube = a3 ∴ a3 = 343 cm3 a = 7 cm Hence, Length of side of cube = 7 cm
Explanation: ∵ Volume of cube = 343 cm3 Let length of side of cube is a then Volume of cube = a3 ∴ a3 = 343 cm3 a = 7 cm Hence, Length of side of cube = 7 cm
143. A right pyramid with square base has side of base 12 cm and height 40 cm. It is kept on its base. It is cut into 4 parts of equal heights by 3 cuts parallel to its base. What is the ratio of volume of the four parts ?
- A. 1 : 8 : 27 : 70
- B. 1 : 7 : 19 : 47
- C. 1 : 7 : 19 : 37
- D. 1 : 8 : 27 : 64
Answer: 1 : 7 : 19 : 37
Explanation: ∴ Squarrel base pyramid is cut in to 4 equal part hence, Ratio of height of each part to side of base will always equal 40 1012 3HeightSide of base= = Volume of part I : Volume of part (I+II) : Volume of part (I+II+III) : Volume of part (I+II+III+IV) = (3)2 × 10 : (6)2 × 20 : (9)2 × 30 : (12)2 × 40 = 1 : 8 : 27 : 64 Part I : Part II : Part III : Part IV = 1 : 7 : 19 : 37
Explanation: ∴ Squarrel base pyramid is cut in to 4 equal part hence, Ratio of height of each part to side of base will always equal 40 1012 3HeightSide of base= = Volume of part I : Volume of part (I+II) : Volume of part (I+II+III) : Volume of part (I+II+III+IV) = (3)2 × 10 : (6)2 × 20 : (9)2 × 30 : (12)2 × 40 = 1 : 8 : 27 : 64 Part I : Part II : Part III : Part IV = 1 : 7 : 19 : 37
144. A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?
- A. 21
- B. 28
- C. 19
- D. 23
Answer: 21
145. A solid cube is cut into three cuboids of same volumes. What is the ratio of the surface area of the cube to the sum of the surface areas of any two of the cuboids so formed?
- A. 27 : 10
- B. 9 : 8
- C. 27 : 16
- D. 9 : 10
Answer: 9 : 10
146. A cube is placed inside a cone of radius 20 cm and height 10 cm, one of its face being on the base of the cone and vertices of opposite face touching the cone. What is the length (in cm) of side of the cube ?
- A. 5
- B. 6
- C. 8
- D. 9
Answer: 8
147. A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area ?
- A. 150
- B. 200
- C. 300
- D. 250
Answer: 200
Explanation: Let, side of original cube = 3cm Side of each of 27 cubes cut = a cm 27(a)3 = (3)3 27(a) 3 = 27 a = 1 According to the question Ratio of surface area = 6 × (3)2 : 27 × 6 × (1)2 = 1 : 3 Required increased percentage 2 100 200%1= × =
Explanation: Let, side of original cube = 3cm Side of each of 27 cubes cut = a cm 27(a)3 = (3)3 27(a) 3 = 27 a = 1 According to the question Ratio of surface area = 6 × (3)2 : 27 × 6 × (1)2 = 1 : 3 Required increased percentage 2 100 200%1= × =
148. Six cubes, each of edge 2 cm, are joined end to end. What is the total surface area of the resulting cuboid in cm2?
- A. 104
- B. 128
- C. 96
- D. 144
Answer: 104
Explanation: ∵ According to question Length of resulting cuboid = 2 × 6 = 12 cm Breadth = 2 cm Height = 2 cm Hence, Total surface area of cuboid = 2 ( lb + bh + hl) = 2(12×2+2×2+2×12) = 2 × 52 = 104 cm2
Explanation: ∵ According to question Length of resulting cuboid = 2 × 6 = 12 cm Breadth = 2 cm Height = 2 cm Hence, Total surface area of cuboid = 2 ( lb + bh + hl) = 2(12×2+2×2+2×12) = 2 × 52 = 104 cm2
149. Five cubes, each of edge 3 cm are joined end to end. What is the total surface area of the resulting cuboid, in cm2?
- A. 280
- B. 244
- C. 270
- D. 198
Answer: 198
Explanation: Length of side of each cube = 3 cm According to the question, Length of resulting cuboid = 3 × 5 = 15 cm Breadth of resulting cuboid = 3 cm Height of resulting cuboid = 3 cm Hence, Total surface area of cuboid = 2 ( lb + bh + hl) = 2 (15 ×3+3×3+3×15) = 2 × 99 = 198 cm 2
Explanation: Length of side of each cube = 3 cm According to the question, Length of resulting cuboid = 3 × 5 = 15 cm Breadth of resulting cuboid = 3 cm Height of resulting cuboid = 3 cm Hence, Total surface area of cuboid = 2 ( lb + bh + hl) = 2 (15 ×3+3×3+3×15) = 2 × 99 = 198 cm 2
150. A solid cube of volume 13824 cm 3 is cut into 8 cube of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is
- A. 8 : 3
- B. 2 : 1
- C. 2 : 3
- D. 4 : 3
Answer: 4 : 3
151. Three cubes each having volume 1728 cm 3 are placed one above the other. What is the total surface area of the resulting solid?
- A. 2304 cm2
- B. 2592 cm2
- C. 2160 cm2
- D. 2016 cm2
Answer: 2016 cm2
152. A prism has a square base whose side is 8 cm. The height of prism is 80 cm. The prism is cut into 10 identical parts by 9 cuts which are parallel to base of prism. What is the total surface area (in cm2) of all the 10 parts together ?
- A. 4260
- B. 2560
- C. 3840
- D. 3220
Answer: 3840
Explanation: ∴ Prism is cut into 10 identical part by 9 cut paral lel to base of prism. Hence, height of each part 80 8cm10= = total surface area of each part = Curved surface area + 2 × Area of base = (Perimeter of base × height) + 2 × area of base = (4 × 8 × 8) + 2 × 8 × 8 = 256 + 128 = 384 cm2 Total surface area of all 10 parts = 384 × 10 = 384 0 cm2
Explanation: ∴ Prism is cut into 10 identical part by 9 cut paral lel to base of prism. Hence, height of each part 80 8cm10= = total surface area of each part = Curved surface area + 2 × Area of base = (Perimeter of base × height) + 2 × area of base = (4 × 8 × 8) + 2 × 8 × 8 = 256 + 128 = 384 cm2 Total surface area of all 10 parts = 384 × 10 = 384 0 cm2
153. A metal cube of edge 18 cm is melted to form three smaller cubes, which are unequal in dimensions. If the edges of two smaller cubes are 9 cm and 15 cm, what is the surface area in (cm2) of the third smaller cube?
- A. 1944
- B. 864
- C. 1728
- D. 486
Answer: 864
Explanation: Volume of bigger cube = [Volume of smaller cubes] (18)3 = (9)3 + (15)3 + x3 5832 = 729 + 3375 + x3 x3 = 5832 - 4104 x3 = 1728 cm3 x = 12 cm. Now, Surface area of third smaller cube = 6x2 = 6×144 = 864 cm 2
Explanation: Volume of bigger cube = [Volume of smaller cubes] (18)3 = (9)3 + (15)3 + x3 5832 = 729 + 3375 + x3 x3 = 5832 - 4104 x3 = 1728 cm3 x = 12 cm. Now, Surface area of third smaller cube = 6x2 = 6×144 = 864 cm 2
154. The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the third number is
- A. 30
- B. 20
- C. 49
- D. 48
Answer: 48
Explanation: Let the three numbers are a, b and c. a : b → (2 : 3) × 5 = 10 : 15 b : c → (5 : 8) × 3 = 15 : 24 a : b : c → 10 : 15 : 24 a + b + c → 49 unit = 98 1 unit = 2 Hence, third number = 24 unit =2 × 24 = 48
Explanation: Let the three numbers are a, b and c. a : b → (2 : 3) × 5 = 10 : 15 b : c → (5 : 8) × 3 = 15 : 24 a : b : c → 10 : 15 : 24 a + b + c → 49 unit = 98 1 unit = 2 Hence, third number = 24 unit =2 × 24 = 48
155. If the volume of a cube is 64 cm 3, then find its total surface area.
- A. 96 cm2
- B. 82 cm2
- C. 88 cm2
- D. 64 cm2
Answer: 96 cm2
Explanation: Volume of cube = a3 a3 = 64 = 43 a = 4 cm, ∵ Total surface area of cube = 6a2 ∴ Total surface area of cube = 6 × (4) 2 = 96 cm2
Explanation: Volume of cube = a3 a3 = 64 = 43 a = 4 cm, ∵ Total surface area of cube = 6a2 ∴ Total surface area of cube = 6 × (4) 2 = 96 cm2
156. If the lateral surface area of cube is 144 cm 2. Then what is the length of its side?
- A. 4 cm
- B. 8 cm
- C. 5 cm
- D. 6 cm
Answer: 6 cm
Explanation: Lateral surface area of cube = 4a2 Now, According to the question - ⇒ 4a 2 = 144 a 2 = 36 Side of cube (a) = 6 cm
Explanation: Lateral surface area of cube = 4a2 Now, According to the question - ⇒ 4a 2 = 144 a 2 = 36 Side of cube (a) = 6 cm
157. What will be the side (in meters) of a cube in which an iron rod of maximum length 10 m can be placed.
- A. 5.57
- B. 7.75
- C. 7.57
- D. 5.77
Answer: 5.77
Explanation: จ Length of diagonal of cube = Maximum length of rod. 3= × Side ง 3 × Side = 10 ง Side of cube 10 10 5.771.7323= = = m
Explanation: จ Length of diagonal of cube = Maximum length of rod. 3= × Side ง 3 × Side = 10 ง Side of cube 10 10 5.771.7323= = = m
158. A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm , breadth 8cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is
- A. 6
- B. 2
- C. 5
- D. 4
Answer: 4
159. The ratio of the total surface area of the cubes is 49 : 81. What is the ratio of their volumes?
- A. 49 : 121
- B. 343 : 729
- C. 294 : 486
- D. 7 : 9
Answer: 343 : 729
Explanation: Let the side of 1st cube = a1 And the side of second cube = a2 According to the question : 2 21 26a : 6a 49 :81= 2 21 2a : a 49 :81= a 1 : a2 = 7 : 9 Ratio of volumes of cubes (a 1)3 : (a2)3 = (7)3 : (9)3 = 343 : 729
Explanation: Let the side of 1st cube = a1 And the side of second cube = a2 According to the question : 2 21 26a : 6a 49 :81= 2 21 2a : a 49 :81= a 1 : a2 = 7 : 9 Ratio of volumes of cubes (a 1)3 : (a2)3 = (7)3 : (9)3 = 343 : 729
160. What is the edge of a cube whose volume is equal to the sum of the volumes of the cubes of edge 6 cm, 8 cm and 10 cm?
- A. 6cm
- B. 12cm
- C. 3cm
- D. 5cm
Answer: 12cm
Explanation: Let the edge of new cube = a cm Volume of new cube = 63 + 83 + 103 a3 = 216 + 512 + 1000 a 3 = 1728 3a 1728 12 cm= =
Explanation: Let the edge of new cube = a cm Volume of new cube = 63 + 83 + 103 a3 = 216 + 512 + 1000 a 3 = 1728 3a 1728 12 cm= =