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321. Find the volume of a cylinder with radius 21cm and height 8cm (π=22/7).
- A. 11088 cm³
- B. 11588 cm³
- C. 10588 cm³
- D. 12088 cm³
Answer: 11088 cm³
Explanation: Volume of a cylinder = πr²h = 22/7 x 21² x 8 = 11088 cm³.
322. A cuboid-shaped water tank of dimensions 6m × 5m × 4m is to be filled. Find its capacity in litres.
- A. 1,50,000 litres
- B. 1,20,000 litres
- C. 1,00,000 litres
- D. 90,000 litres
Answer: 1,20,000 litres
Explanation: Volume of the cuboid tank = l x b x h = 6 x 5 x 4 = 120 m³. As 1 m³ = 1000 litres, capacity = 120 x 1000 = 120000 litres.
323. Find the volume of a cube with side 11cm.
- A. 726 cm³
- B. 1301 cm³
- C. 1331 cm³
- D. 1361 cm³
Answer: 1331 cm³
Explanation: Volume of a cube = a³ = 11³ = 1331 cm³.
324. Find the area of a sector of a circle with radius 21cm and central angle 60° (π=22/7).
- A. 115.5 cm²
- B. 231 cm²
- C. 346.5 cm²
- D. 462 cm²
Answer: 231 cm²
Explanation: Sector area = (θ/360) x πr² = (60/360) x 22/7 x 21² = 231 cm².
325. Find the volume of a cube with side 9cm.
- A. 486 cm³
- B. 729 cm³
- C. 699 cm³
- D. 759 cm³
Answer: 729 cm³
Explanation: Volume of a cube = a³ = 9³ = 729 cm³.
326. Find the area of a sector of a circle with radius 14cm and central angle 90° (π=22/7).
- A. 308 cm²
- B. 154 cm²
- C. 77 cm²
- D. 196 cm²
Answer: 154 cm²
Explanation: Sector area = (θ/360) x πr² = (90/360) x 22/7 x 14² = 154 cm².
327. Find the volume of a cube with side 7cm.
- A. 343 cm³
- B. 313 cm³
- C. 294 cm³
- D. 373 cm³
Answer: 343 cm³
Explanation: Volume of a cube = a³ = 7³ = 343 cm³.
328. The circumference of a circle is 88cm. Find its radius (π=22/7).
- A. 16cm
- B. 14cm
- C. 10cm
- D. 12cm
Answer: 14cm
Explanation: Circumference = 2πr, so r = C/(2π) = 88 x 7/44 = 14 cm.
329. Find the volume of a cuboid with length 12cm, breadth 8cm, height 6cm.
- A. 600 cm³
- B. 560 cm³
- C. 576 cm³
- D. 540 cm³
Answer: 576 cm³
Explanation: Volume of a cuboid = l x b x h = 12 x 8 x 6 = 576 cm³.
330. The area of a circle is 154 cm². Find its radius (π=22/7).
- A. 7cm
- B. 8cm
- C. 9cm
- D. 6cm
Answer: 7cm
Explanation: Area = πr², so r² = 154 x 7/22 = 49 and r = 7 cm.
331. Find the surface area of a sphere with radius 14cm (π=22/7).
- A. 2464 cm²
- B. 2200 cm²
- C. 2500 cm²
- D. 2400 cm²
Answer: 2464 cm²
Explanation: Surface area of a sphere = 4πr² = 4 x 22/7 x 14² = 2464 cm².
332. Find the curved surface area of a hemisphere with radius 14cm (π=22/7).
- A. 1848 cm²
- B. 1232 cm²
- C. 2464 cm²
- D. 616 cm²
Answer: 1232 cm²
Explanation: Curved surface area of a hemisphere = 2πr² = 2 x 22/7 x 14² = 1232 cm². The total surface area would add the flat base (3πr²), so it is not the same.
333. Find the volume of a sphere with radius 21cm (π=22/7).
- A. 36000 cm³
- B. 38808 cm³
- C. 40000 cm³
- D. 37000 cm³
Answer: 38808 cm³
Explanation: Volume of a sphere = (4/3)πr³ = (4/3) x 22/7 x 21³ = 38808 cm³.
334. Find the volume of a hemisphere with radius 21cm (π=22/7).
- A. 9,702 cm³
- B. 19,404 cm³
- C. 18,000 cm³
- D. 38,808 cm³
Answer: 19,404 cm³
Explanation: Volume of a hemisphere = (2/3)πr³ = (2/3) x 22/7 x 21³ = 19404 cm³. The full sphere would be double this.
335. Find the curved surface area of a cylinder with radius 7cm and height 20cm (π=22/7).
- A. 900 cm²
- B. 800 cm²
- C. 880 cm²
- D. 840 cm²
Answer: 880 cm²
Explanation: Curved surface area of a cylinder = 2πrh = 2 x 22/7 x 7 x 20 = 880 cm².
336. The volume of a cube is 1000 cm³. Find its total surface area.
- A. 500 cm²
- B. 1000 cm²
- C. 400 cm²
- D. 600 cm²
Answer: 600 cm²
Explanation: Side = ∛1000 = 10 cm. Total surface area of a cube = 6a² = 6 x 10² = 600 cm².
337. Find the total surface area of a cube with side 8cm.
- A. 360 cm²
- B. 400 cm²
- C. 384 cm²
- D. 320 cm²
Answer: 384 cm²
Explanation: A cube has 6 equal square faces, so total surface area = 6a² = 6 x 8² = 384 cm².
338. The volume of a cube is 343 cm³. Find the length of its side.
- A. 9cm
- B. 7cm
- C. 8cm
- D. 6cm
Answer: 7cm
Explanation: Volume of a cube = a³, so a = ∛343 = 7 cm because 7³ = 343.
339. Find the volume of a cone with radius 9cm and height 21cm (π=22/7).
- A. 1650 cm³
- B. 1782 cm³
- C. 1800 cm³
- D. 1700 cm³
Answer: 1782 cm³
Explanation: Volume of a cone = (1/3)πr²h = (1/3) x 22/7 x 9² x 21 = 1782 cm³.
340. A cylindrical tank has radius 7m and height 10m. Find its capacity in litres (π=22/7, 1m³=1000L).
- A. 14,00,000 litres
- B. 16,00,000 litres
- C. 15,40,000 litres
- D. 15,00,000 litres
Answer: 15,40,000 litres
Explanation: Capacity = πr²h = 22/7 x 7² x 10 = 1540 m³. Since 1 m³ = 1000 L, it holds 1540 x 1000 = 1540000 litres.
341. Find the volume of a cylinder with radius 14cm and height 15cm (π=22/7).
- A. 9500 cm³
- B. 8800 cm³
- C. 9240 cm³
- D. 9000 cm³
Answer: 9240 cm³
Explanation: Volume of a cylinder = πr²h = 22/7 x 14² x 15 = 9240 cm³.
342. Find the total surface area of a cuboid with length 10cm, breadth 8cm, height 6cm.
- A. 480 cm²
- B. 376 cm²
- C. 396 cm²
- D. 340 cm²
Answer: 376 cm²
Explanation: Total surface area of a cuboid = 2(lb + bh + hl) = 2(80 + 48 + 60) = 376 cm².
343. Find the volume of a cube with side 6cm.
- A. 216 cm³
- B. 196 cm³
- C. 180 cm³
- D. 225 cm³
Answer: 216 cm³
Explanation: Volume of a cube = a³ = 6³ = 216 cm³.
344. Find the lateral surface area of a cuboid with length 8cm, breadth 6cm, height 5cm.
- A. 140 cm²
- B. 120 cm²
- C. 96 cm²
- D. 236 cm²
Answer: 140 cm²
Explanation: Lateral surface area of a cuboid = 2h(l + b) = 2 x 5 x (8 + 6) = 140 cm², which leaves out the top and bottom faces.
345. Find the area of a trapezium with parallel sides 10cm and 14cm, and height 6cm.
- A. 72 cm²
- B. 144 cm²
- C. 60 cm²
- D. 84 cm²
Answer: 72 cm²
Explanation: Area of a trapezium = (1/2) x (sum of parallel sides) x height = 0.5 x (10 + 14) x 6 = 72 cm².
346. Find the lateral surface area of a cube with side 9cm.
- A. 729 cm²
- B. 162 cm²
- C. 486 cm²
- D. 324 cm²
Answer: 324 cm²
Explanation: Lateral surface area of a cube = 4a² (four side faces) = 4 x 9² = 324 cm². The total surface area would be 6a², so the top and bottom are excluded here.
347. Find the volume of a cuboid with length 10cm, breadth 5cm, height 4cm.
- A. 190 cm³
- B. 200 cm³
- C. 180 cm³
- D. 220 cm³
Answer: 200 cm³
Explanation: Volume of a cuboid = l x b x h = 10 x 5 x 4 = 200 cm³.
348. Find the area of an equilateral triangle with side 10cm (√3=1.73).
- A. 50 cm²
- B. 40 cm²
- C. 43.25 cm²
- D. 36 cm²
Answer: 43.25 cm²
Explanation: Area of an equilateral triangle = (√3/4)a² = (1.73/4) x 10² = 43.25 cm², which matches the closest listed value of 43.25 cm².
349. Find the surface area of a sphere with radius 7cm (π=22/7).
- A. 600 cm²
- B. 616 cm²
- C. 588 cm²
- D. 630 cm²
Answer: 616 cm²
Explanation: Surface area of a sphere = 4πr² = 4 x 22/7 x 7² = 616 cm².
350. Find the area of an equilateral triangle with side 8cm (√3=1.73).
- A. 24 cm²
- B. 32 cm²
- C. 16 cm²
- D. 27.71 cm²
Answer: 27.71 cm²
Explanation: Area of an equilateral triangle = (√3/4)a² = (1.73/4) x 8² = 27.68 cm², which matches the closest listed value of 27.71 cm².
351. Find the volume of a sphere with radius 7cm (π=22/7).
- A. 1400 cm³
- B. ≈1437.33 cm³
- C. 1386 cm³
- D. 1500 cm³
Answer: ≈1437.33 cm³
Explanation: Volume of a sphere = (4/3)πr³ = (4/3) x 22/7 x 7³ = 1437.33 cm³.
352. The perimeter of a rhombus with diagonals 12cm and 16cm is:
- A. 28cm
- B. 48cm
- C. 56cm
- D. 40cm
Answer: 40cm
Explanation: The diagonals bisect each other at right angles, so side = √((12/2)² + (16/2)²) = √(36 + 64) = 10 cm. Perimeter = 4 x 10 = 40 cm.
353. Find the curved surface area of a cylinder with radius 7cm and height 10cm (π=22/7).
- A. 440 cm²
- B. 460 cm²
- C. 420 cm²
- D. 400 cm²
Answer: 440 cm²
Explanation: Curved surface area of a cylinder = 2πrh = 2 x 22/7 x 7 x 10 = 440 cm².
354. The area of a rhombus with diagonals 16cm and 24cm is:
- A. 192 cm²
- B. 200 cm²
- C. 384 cm²
- D. 168 cm²
Answer: 192 cm²
Explanation: Area of a rhombus = (1/2) x d1 x d2 = 0.5 x 16 x 24 = 192 cm². Without the half factor you would get 384, which is the tempting wrong value.
355. Find the total surface area of a cube with side 6cm.
- A. 225 cm²
- B. 180 cm²
- C. 196 cm²
- D. 216 cm²
Answer: 216 cm²
Explanation: A cube has 6 equal square faces, so total surface area = 6a² = 6 x 6² = 216 cm².
356. Find the curved surface area of a cone with radius 21cm and slant height 28cm (π=22/7).
- A. 1936 cm²
- B. 1848 cm²
- C. 1760 cm²
- D. 1680 cm²
Answer: 1848 cm²
Explanation: Curved surface area of a cone = πrl = 22/7 x 21 x 28 = 1848 cm².
357. A cone and a cylinder have equal base and equal height. Find the ratio of volume of cone to cylinder.
- A. 1:3
- B. 2:3
- C. 1:4
- D. 1:2
Answer: 1:3
Explanation: Cone volume is (1/3)πr²h and cylinder volume is πr²h for equal base and height, so the ratio is (1/3):1 = 1:3. A cone always holds exactly one-third of the cylinder it fits in.
358. Find the total surface area of a cone with radius 7cm and slant height 25cm (π=22/7).
- A. 628 cm²
- B. 770 cm²
- C. 550 cm²
- D. 704 cm²
Answer: 704 cm²
Explanation: Total surface area of a cone = πr(l + r) = 22/7 x 7 x (25 + 7) = 704 cm², which includes the base as well as the curved part.
359. Find the volume of a cone with radius 6cm and height 14cm (π=22/7).
- A. 550 cm³
- B. 500 cm³
- C. 480 cm³
- D. 528 cm³
Answer: 528 cm³
Explanation: Volume of a cone = (1/3)πr²h = (1/3) x 22/7 x 6² x 14 = 528 cm³.
360. Find the total surface area of a cylinder with radius 14cm and height 20cm (π=22/7).
- A. 3080 cm²
- B. 2860 cm²
- C. 2992 cm²
- D. 2640 cm²
Answer: 2992 cm²
Explanation: Total surface area of a cylinder = 2πr(r + h) = 2 x 22/7 x 14 x (14 + 20) = 2992 cm², covering both circular ends and the curved side.
361. Find the volume of a cylinder with radius 7cm and height 10cm (π=22/7).
- A. 1440 cm³
- B. 1340 cm³
- C. 1640 cm³
- D. 1540 cm³
Answer: 1540 cm³
Explanation: Volume of a cylinder = πr²h = 22/7 x 7² x 10 = 1540 cm³.
362. Find the total surface area of a cylinder with radius 7cm and height 10cm (π=22/7).
- A. 770 cm²
- B. 700 cm²
- C. 660 cm²
- D. 748 cm²
Answer: 748 cm²
Explanation: Total surface area of a cylinder = 2πr(r + h) = 2 x 22/7 x 7 x (7 + 10) = 748 cm², covering both circular ends and the curved side.
363. Find the volume of a cube with side 5cm.
- A. 100 cm³
- B. 125 cm³
- C. 75 cm³
- D. 150 cm³
Answer: 125 cm³
Explanation: Volume of a cube = a³ = 5³ = 125 cm³.
364. Find the volume of a cone with radius 3.5cm and height 12cm (π=22/7).
- A. 144 cm³
- B. 154 cm³
- C. 164 cm³
- D. 132 cm³
Answer: 154 cm³
Explanation: Volume of a cone = (1/3)πr²h = (1/3) x 22/7 x 3.5² x 12 = 154 cm³.
365. What is the total surface area of the cone? I. The area of the base of the cone is 154 cm2. II. The curved surface area of the cone is 550 cm2. III. The volume of the cone is 1232 cm3.
- A. I, and either II or III
- B. II, and either I or III
- C. III, and either I or II
- D. Any two of the three
Answer: I, and either II or III
Explanation: Total surface area of the cone = (πrl + πr2) cm2. I. gives, πr2 = 154. Thus, we can find r. II. gives, πrl = 550. From I and II we get the answer. III. gives, 1 2 1232. 3 π= rh From I and III, we can find h and therefore, l. Hence the surface area can be determined. ∴ Correct answer is (a).
366. A solid metallic cone is melted and recast into a sphere. What is the radius of the sphere? I. The radius of the base of the cone is 2.1 cm. II. The height of the cone is four times the radius of its base. III. The height of the cone is 8.4 cm.
- A. Only I and II
- B. Only II and III
- C. Only I and III
- D. Any two of the three
Answer: Any two of the three
Explanation: 41 32 . 33 π =π R rh Now r and h can be determined from any two of I, II and III. Thus, R can be calculated. ∴ Correct answer is (d).
367. What is the capacity of the cylindrical tank? (Bank. P.O., 2008) I. Radius of the base is half of its height. II. Area of the base is 616 square metres. III. Height of the cylinder is 28 metres.
- A. Only I and II
- B. Only II and III
- C. Only I and III
- D. Any two of the three
Answer: Any two of the three
368. What is the capacity of the cylindrical tank? I. The area of the base is 61,600 sq. cm. II. The height of the tank is 1.5 times the radius. III. The circumference of base is 880 cm.
- A. Only I and II
- B. Only II and III
- C. Only I and III
- D. Only II and either I or III
Answer: Only II and either I or III
Explanation: Capacity = πr2h. I. gives, πr2 = 61600. This gives r. II. gives, h = 1.5 r. Thus, I and II give the answer. Again, III. gives 2πr = 880. This gives r. So, II and III also give the answer. ∴ Correct answer is (e).
369. What is the ratio of the volume of the given right circular cone to the one obtained from it? I. The smaller cone is obtained by passing a plane parallel to the base and dividing the original height in the ratio 1 : 2. II. The height and the base of the new cone are one-third those of the original cone.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
370. A spherical ball of given radius x cm is melted and made into a right circular cylinder. What is the height of the cylinder? I. The volume of the cylinder is equal to the volume of the ball. II. The area of the base of the cylinder is given.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
Explanation: Clearly, I is not needed, since it is evident from the given question. From II, we get radius of the base of the cylinder. Now, 4 32 3 π =π x rh in which x and r are known. ∴ h can be determined. ∴ Correct answer is (b).
371. Is a given rectangular block, a cube? I. At least 2 faces of the rectangular block are squares. II. The volume of the block is 64.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data given in both Statements I and II together are not sufficient to answer the question.
Explanation: I. gives, any two of l, b, h are equal. II. gives, lbh = 64. From I and II, the values of l, b, h may be (1, 1, 64), (2, 2, 16), (4, 4, 4). Thus, the block may be a cube or cuboid. ∴ Correct answer is (d).
372. What will be the total cost of whitewashing the coni-cal tomb at the rate of 80 paise per square metre? I. The diameter and the slant height of the tomb are 28 m and 50 m. II. The height of the tomb is 48 m and the area of its base is 616 sq. m.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
373. What is the volume of the cylinder? I. Height is equal to the diameter. II. Perimeter of the base is 352 cm.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
374. What is the capacity of a cylindrical tank? I. Radius of the base is half of its height which is 28 metres. II. Area of the base is 616 sq. metres and its height is 28 metres.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
Explanation: I. gives, h = 28 m and r = 14 cm. ∴ Capacity = πr2h, which can be obtained. Thus, I alone gives the answer. II. gives, πr2 = 616 m2 and h = 28 m. ∴ Capacity = (πr2 × h) = (616 × 28) m3. Thus, II alone gives the answer. ∴ Correct answer is (c).
375. What is the total cost of painting the in-ner surface of an open box at the rate of 50 paise per 100 sq. cm? I. The box is made of wood 3 cm thick. II. The external dimensions of the box are 50 cm, 40 cm and 23 cm.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
376. How much cardboard will it take to make an open cubical box with no top? I. The area of the bottom of the box is 4 square meters. II. The volume of the box is 8 cubic metres.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
Explanation: I. Let the length of each edge of the box be a metres. Then, a2 = 4 ⇒ a = 2 m. ∴ Area of the cardboard needed = 5a2 = (5 × 22) m2 = 20 m2. Thus, I alone gives the answer. II. a3 = 8 ⇒ a = 2 m. ∴ Required area = 5a2 = (5 × 22) m2 = 20 m2. Thus, II alone gives the answer. So, correct answer is (c).
377. What is the volume of a cube? I. The area of each face of the cube is 64 square metres. II. The length of one side of the cube is 8 metres.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
Explanation: Let each edge be a metres. Then, I. a2 = 64 ⇒ a = 8 m ⇒ Volume = (8 × 8 × 8) m3 = 512 m3. Thus, I alone gives the answer. II. a = 8 m ⇒ Volume = (8 × 8 × 8) m3 = 512 m3. Thus, II alone gives the answer. ∴ Correct answer is (c).
378. What is the volume of 32 metre high cylindrical tank? I. The area of its base is 154 m2. II. The diameter of the base is 14 m.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data given in both Statements I and II together are not sufficient to answer the question.
Answer: If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
379. What is the weight of the iron beam? I. The beam is 9 m long, 40 cm wide and 20 cm high. II. Iron weighs 50 kg per cubic metre.
- A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
- B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
- C. If the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
- D. If the data in both Statements I and II together are necessary to answer the question.
Answer: If the data in both Statements I and II together are necessary to answer the question.
380. A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6cm and 8cm, find the edges of the third smaller cube.
- A. 8 cm
- B. 10 cm
- C. 12 cm
- D. None of these
Answer: 10 cm
381. A swimming pool 9m wide and 12m long and 1m deep on the shallow side and 4m deep on the deeper side. Its volume is
- A. 360 m3
- B. 270 m3
- C. 420 m3
- D. None of these
Answer: 270 m3
382. When a ball bounces, it rises to 2 3 of the height from which it fell. If the ball is dropped from a height of 36 m, how high will it rise at the third bounce?
- A. 10 1 3 m
- B. 10 23 m
- C. 12 1 3 m
- D. 12 23 m
Answer: 10 23 m
383. If the radius of a sphere is increased by 10%, then the volume will be increased by
- A. 33.1%
- B. 30%
- C. 50%
- D. 10%
Answer: 33.1%
384. If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere, then the diameter of the new sphere will be
- A. 12 cm
- B. 24 cm
- C. 30 cm
- D. 36 cm
Answer: 24 cm
385. A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is
- A. 3.5 cm
- B. 5 cm
- C. 7 cm
- D. 14 cm
Answer: 7 cm
386. The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is
- A. 2 : 1 / 2: 1
- B. 1 : 2 / 1: 2
- C. 2 : 3 / 2: 3
- D. 3 : 2 / 3: 2
Answer: 2 : 1 / 2: 1
387. A sphere and a cube have same surface area. The ratio of squares of their volumes is
- A. 6 : π / 6: π
- B. 5 : π / 5: π
- C. 3 : 5 / 3: 5
- D. 1 : 1 / 1: 1
Answer: 6 : π / 6: π
388. A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm. How much soup the hospital has to prepare daily to serve 250 patients?
- A. 38L
- B. 40L
- C. 39.5L
- D. 35.5L
Answer: 35.5L
389. A solid piece of iron is in the form of a cuboids of dimensions (49cm × 33cm × 24cm) is melted and moulded to form a solid sphere. The radius of the sphere is
- A. 19cm
- B. 21cm
- C. 23cm
- D. 25cm
Answer: 21cm
390. The sum of the radius and the height of a cylinder is 19 m. The total surface area of the cylinder is 1672m2, what is the volume of the cylinder? (in m3)
- A. 3080
- B. 2940
- C. 3220
- D. 2660
Answer: 3080
391. The base of a right prism is a trapezium whose lengths of two parallels sides are 10 cm and 6cm and distance between them is 5 cm. If the heights of the prism is 8cm, its volume is
- A. 320 cm3
- B. 300 cm3
- C. 310 cm3
- D. 300.5 cm3
Answer: 320 cm3
392. Each side of a cube is decreased by 25%. Find the ratio of the volumes of the original cube and the resulting cube.
- A. 64 : 1 / 64: 1
- B. 27 : 64 / 27: 64
- C. 64 : 27 / 64: 27
- D. 8 : 1 / 8: 1
Answer: 64 : 27 / 64: 27
393. If the volume and curved surfaces area of a cylinder are 616 m3 and 352m2 respectively, what is the total surface area of the cylinder (in m2)
- A. 429
- B. 419
- C. 435
- D. 421
Answer: 429
394. A hemispherical bowls has 3.5cm radius. It is to be painted inside as well as outside. The cost of paint-ing it at the rate of ₹ 5 per 10sq. cm will be
- A. ₹ 77
- B. ₹ 100
- C. ₹ 175
- D. ₹ 50
Answer: ₹ 77
395. The radius of a cylinder is 5m more than its height. If the curved surface area of the cylinder is 792m2, what is the volume of the cylinder? (in m3)
- A. 5712
- B. 5244
- C. 5544
- D. 5306
Answer: 5544
396. Base of a right prism is a rectangle, the ratio of whose length and breadth is 3 : 2. If the height of the prism is 12 cm and total surface area is 288 sq. cm. the volume of the prism is
- A. 291cm3
- B. 288cm3
- C. 290cm3
- D. 286cm3
Answer: 288cm3
397. The volume of a right circular cone which is obtained from a wooden cube of edge 4.2 dm wasting minimum amount of wood is
- A. 19404 dm3
- B. 194.04 dm3
- C. 19.404 dm3
- D. 1940.4 dm3
Answer: 19.404 dm3
398. Length of each edge, of a regular tetrahedron is 1 cm. Its volume is
- A. 3 12 cm3
- B. 1 34 cm3
- C. 2 6 cm3
- D. 1 212 cm3
Answer: 1 212 cm3
399. A right pyramid has an equilateral triangular base of side 4 units. If the number of square units of its whole surface area is three times the number of cubic units of its volume, find its height.
- A. 3 units
- B. 4 units
- C. 5 units
- D. 6 units
Answer: 4 units
400. A pyramid has an equilateral triangle as its base of which each side is 1m. Its slant edge is 3 m. The whole surface area of the pyramid is equal to
- A. 3 2 13 + sq. m 4
- B. 3 3 13 + sq. m 4
- C. 3 3 35 + sq. m 4
- D. 3 2 35 + sq. m 4
Answer: 3 3 35 + sq. m 4
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