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481. A solid metallic right circular cylinder of base di-ameter 16 cm and height 2 cm is melted and recast into a right circular cone of height three times that of the cylinder. Find the curved surface area of the cone. [Use p = 3.14]
- A. 196.8 cm2
- B. 228.4 cm2
- C. 251.2 cm2
- D. None of these
Answer: 251.2 cm2
482. The radius of the base and height of a metallic solid cylinder are r cm and 6 cm respectively. It is melted and recast into a solid cone of the same radius of base. The height of the cone is
- A. 9 cm
- B. 18 cm
- C. 27 cm
- D. 54 cm
Answer: 18 cm
483. A conical cavity is drilled in a circular cylinder of 15 cm height and 16 cm base diameter. The height and base diameter of the cone are the same as those of the cylinder. Determine the total surface area of the remaining solid.
- A. 215 p cm2
- B. 376 p cm2
- C. 440 p cm2
- D. 542 p cm2
Answer: 440 p cm2
484. A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is
- A. 3 : 1 / 3: 1
- B. 13 : 9 / 13: 9
- C. 17 : 9 / 17: 9
- D. 34 : 9 / 34: 9
Answer: 17 : 9 / 17: 9
485. A cone of height 7 cm and base radius 3 cm is carved from a rectangular block of wood 10 cm × 5 cm × 2 cm. The percentage of wood wasted is
- A. 34%
- B. 46%
- C. 54%
- D. 66%
Answer: 34%
486. Find the volume of the largest right circular cone that can be cut out from a cube whose edge is 9 cm.
- A. 170.93 cm3
- B. 180.93 cm3
- C. 190.93 cm3
- D. 200.93 cm3
Answer: 190.93 cm3
487. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ratio of their heights will be
- A. 3 : 4 / 3: 4
- B. 4 : 3 / 4: 3
- C. 3 : 8 / 3: 8
- D. 8 : 3 / 8: 3
Answer: 8 : 3 / 8: 3
488. The radii of two cones are in the ratio 2 : 1, their volumes are equal. Find the ratio of their heights.
- A. 1 : 8 / 1: 8
- B. 1 : 4 / 1: 4
- C. 2 : 1 / 2: 1
- D. 4 : 1 / 4: 1
Answer: 1 : 4 / 1: 4
Explanation: Let their radii be 2x, x and their heights be h and H re-spectively. Then, 11 1 2 2 (2 ) or . 33 4h x h xH H ×π× × = ×π× × =
489. If the heights of two cones are in the ratio 7 : 3 and their diameters are in the ratio 6 : 7, what is the ratio of their volumes?
- A. 3 : 7 / 3: 7
- B. 4 : 7 / 4: 7
- C. 5 : 7 / 5: 7
- D. 12 : 7 / 12: 7
Answer: 12 : 7 / 12: 7
490. If the height, curved surface area and the volume of a cone are h, c and v respectively, then 3p vh3 – c2h2 + 9v2 will be equal to
- A. 0
- B. 1
- C. chv
- D. v2h
Answer: 0
491. If the height of a cone be doubled and radius of base remains the same, then the ratio of the volume of the given cone to that of the second cone will be
- A. 1 : 2 / 1: 2
- B. 2 : 1 / 2: 1
- C. 1 : 8 / 1: 8
- D. 8 : 1 / 8: 1
Answer: 1 : 2 / 1: 2
492. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone
- A. remains unaltered
- B. decreases by 25%
- C. increases by 25%
- D. increases by 50%
Answer: decreases by 25%
493. If both the radius and height of a right circular cone are increased by 20%, its volume will be increased by
- A. 20%
- B. 40%
- C. 60%
- D. 72.8%
Answer: 72.8%
494. If the height of a cone is doubled and its base diameter is trebled, then the ratio of the volume of the resultant cone to that of the original cone is
- A. 6 : 1 / 6: 1
- B. 9 : 1 / 9: 1
- C. 9 : 2 / 9: 2
- D. 18 : 1 / 18: 1
Answer: 18 : 1 / 18: 1
495. The length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 sq. m is
- A. 490 m
- B. 525 m
- C. 665 m
- D. 860 m
Answer: 525 m
496. A semicircular sheet of paper of diameter 28 cm is bent to cover the exterior surface of an open conical ice-cream cup. The depth of the ice-cream cup is
- A. 8.12 cm
- B. 10.12 cm
- C. 12.12 cm
- D. 14.12 cm
Answer: 12.12 cm
497. A vertical cone of volume V with vertex downwards is filled with water upto half of its height. The vol-ume of the water is
- A. 2 V
- B. 4V
- C. 8 V
- D. 16V
Answer: 8 V
498. The radius and height of a right circular cone are in the ratio 3 : 4. If its volume is 5 3 301 cm , 7 what is its slant height?
- A. 8 cm
- B. 9 cm
- C. 10 cm
- D. 12 cm
Answer: 10 cm
499. Volume of a right circular cone having base radius 70 cm and curved surface area 40040 cm2 is
- A. 823400 cm3
- B. 824000 cm3
- C. 840000 cm3
- D. 862400 cm3
Answer: 862400 cm3
500. If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, then the curved surface area of the cone is
- A. 10001 cm2
- B. 10010 cm2
- C. 10100 cm2
- D. 11000 cm2
Answer: 10010 cm2
501. The slant height of a conical mountain is 2.5 km and the area of its base is 1.54 km2. The height of the mountain is
- A. 2.2 km
- B. 2.4 km
- C. 3 km
- D. 3.11 km
Answer: 2.4 km
502. Area of the canvas cloth needed to erect a right conical tent of height 12 ft and circular base having circumference 10p ft is
- A. 60 sq ft
- B. 65 sq ft
- C. 65p sq ft
- D. 120p sq ft
Answer: 65p sq ft
Explanation: Let the radius of base be r ft. Then, 2pr = 10p or r = 5. l = 22 2 2 rh += + = = 5 (12) 169 13 ft. ∴ Area of cloth = prl = (p × 5 × 13) sq ft = 65 p sq ft.
503. A conical tent is to accommodate 11 persons. Each person must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breathe. The height of the cone is
- A. 13 m
- B. 14 m
- C. 15 m
- D. 16 m
Answer: 15 m
504. If a right circular cone of height 24 cm has a volume of 1232 cm3, then the area of its curved surface is
- A. 154 cm2
- B. 550 cm2
- C. 704 cm2
- D. 1254 cm2
Answer: 550 cm2
505. The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.
- A. 30π m2
- B. 40π m2
- C. 60π m2
- D. 80π m2
Answer: 60π m2
506. A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 3 cm to form a cone. The volume of the cone so formed is
- A. 12π cm3
- B. 15π cm3
- C. 16π cm3
- D. 20π cm3
Answer: 12π cm3
507. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
- A. 344.35 cm2
- B. 462 cm2
- C. 498.35 cm2
- D. None of these
Answer: 498.35 cm2
508. The curved surface of a right circular cone of height 15 cm and base diameter 16 cm is
- A. 60π cm2
- B. 68π cm2
- C. 120π cm2
- D. 136π cm2
Answer: 136π cm2
509. The curved surface of a right circular cone of height 84 cm and base diameter 70 cm is
- A. 1001 cm2
- B. 9900 cm2
- C. 10001 cm2
- D. 10010 cm2
Answer: 10010 cm2
510. Find the slant height of the cone whose height is 4.8 cm and the diameter of base is 4 cm.
- A. 4.2 cm
- B. 5.2 cm
- C. 6.2 cm
- D. 7.2 cm
Answer: 5.2 cm
Explanation: Radius, r = 2 cm. Height, h = 4.8 cm. ∴ Slant height, l = 22 2 2 rh += + 2 (4.8) cm = 4 23.04 cm = 27.04 cm = 5.2 cm. +
511. What is the weight of water contained in a conical vessel 21 cm deep and 16 cm in diameter?
- A. 1.256 kg
- B. 1.408 kg
- C. 2.480 kg
- D. 3.875 kg
Answer: 1.408 kg
512. The radius of the base and height of a cone are 3 cm and 5 cm respectively whereas the radius of the base and height of a cylinder are 2 cm and 4 cm respectively. The ratio of the volume of cone to that of the cylinder is
- A. 1 : 3 / 1: 3
- B. 15 : 8 / 15: 8
- C. 15 : 16 / 15: 16
- D. 45 : 16 / 45: 16
Answer: 15 : 16 / 15: 16
513. A circular cylinder can hold 61.6 c.c. of water. If the height of the cylinder is 40 cm and the outer diameter is 16 mm, then the thickness of the material of the cylinder is
- A. 0.2 mm
- B. 0.3 mm
- C. 1 mm
- D. 2 mm
Answer: 1 mm
514. A milkman saves milk in two vessels, a cuboidal and the other a cylindrical one. The capacity of the cuboidal vessel is 20 litres more than the cylinddrical one. When 30 litres of milk is drawn from each of the two full vessels, the amount left in the cuboidal vessel is twice that left in the cylindrical vessel. The capacity (in litres) of the cuboidal vessel is
- A. 30
- B. 50
- C. 70
- D. 130
Answer: 70
Explanation: Let the capacity of the cylindrical vessel be x litres. Then, capacity of the cuboidal vessel = (x + 20) litres. ∴ (x + 20) – 30 = 2(x – 30) ⇒ x – 10 = 2x – 60 ⇒ x = 50.
515. 1496 cm3 of metal is used to cast a pipe of length 28 cm. If the internal radius of the pipe is 8 cm, the outer radius of the pipe is
- A. 7 cm
- B. 9 cm
- C. 10 cm
- D. 12 cm
Answer: 9 cm
516. A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is
- A. 3.6 kg
- B. 3.696 kg
- C. 36 kg
- D. 36.9 kg
Answer: 3.696 kg
517. What length of solid cylinder 2 cm in diameter must be taken to cast into a hollow cylinder of external diameter 12 cm, 0.25 cm thick and 15 cm long?
- A. 42.3215 cm
- B. 44.0123 cm
- C. 44.0625 cm
- D. 44.6023 cm
Answer: 44.0625 cm
518. A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm. The metal everywhere is 0.4 cm thick. The volume of the metal is
- A. 280.52 cm3
- B. 306.24 cm3
- C. 310 cm3
- D. 316 cm3
Answer: 306.24 cm3
519. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of the iron used is
- A. 54982 cm3
- B. 56372 cm3
- C. 57636 cm3
- D. 58752 cm3
Answer: 58752 cm3
520. An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe is
- A. 3068 cm2
- B. 3168 cm2
- C. 3268 cm2
- D. 3368 cm2
Answer: 3168 cm2
521. Rain water, which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if a rainfall of 1 cm has fallen?
- A. 188 cm
- B. 189 cm
- C. 190 cm
- D. 191 cm
Answer: 191 cm
522. The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelopiped on a square base is
- A. 44 m3
- B. 45 m3
- C. 46 m3
- D. 47 m3
Answer: 45 m3
523. Water is flowing at the rate of 5 km/hr through a cylindrical pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time in which the level of water in the tank will rise by 7 cm.
- A. 1 hour
- B. 1 1 hours 2
- C. 2 hours
- D. 3 hours
Answer: 2 hours
524. What part of a ditch, 48 metres long, 16.5 metres broad and 4 metres deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 metres and length 56 metres ?
- A. 1 9
- B. 29
- C. 7 9
- D. 89
Answer: 29
525. The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions ?
- A. 36 m2
- B. 40 m2
- C. 44 m2
- D. 48 m2
Answer: 44 m2
526. A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire is,
- A. 1 15
- B. 130
- C. 2 15
- D. 15
Answer: 130
527. 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be
- A. 84
- B. 90
- C. 168
- D. 336
Answer: 84
528. Two cylindrical vessels with radii 15 cm and 10 cm and heights 35 cm and 15 cm respectively are filled with water. If this water is poured into a cylindrical vessel 15 cm in height, then the radius of the vessel is
- A. 17.5 cm
- B. 18 cm
- C. 20 cm
- D. 25 cm
Answer: 25 cm
529. Find the number of coins 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
- A. 430
- B. 440
- C. 450
- D. 460
Answer: 450
530. The number of circular pipes with an inside diameter of 1 inch which will carry the same amount of water as a pipe with an inside diameter of 6 inches is
- A. 6p
- B. 12
- C. 36
- D. 36p
Answer: 36
531. Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?
- A. 2 m
- B. 3 m
- C. 4 m
- D. 5 m
Answer: 3 m
532. The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe with a velocity of 5 m/sec. How many minutes will it take in filling the cistern with water ?
- A. 20
- B. 40
- C. 60
- D. 80
Answer: 80
533. Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per second. If the pipe is always half full, then what is the volume of water (in litres) discharged in 10 minutes?
- A. 2310
- B. 3850
- C. 4620
- D. 9240
Answer: 4620
534. A well with inner diameter 8 m is dug 14 m deep. Earth taken out of its has been evenly spread all around it to a width of 3 m to form an embankment. The height of the embankment will be
- A. 26 4 m 33
- B. 26 5 cm33
- C. 26 6 cm 33
- D. 26 7 cm33
Answer: 26 6 cm 33
535. A cylindrical tank of diameter 35 cm is full of water. If 11 litres of water is drawn off, the water level in the tank will drop by
- A. 1 10 cm 2
- B. 3 11 cm7
- C. 6 12 cm 7
- D. 14 cm
Answer: 3 11 cm7
536. Diameter of a jar cylindrical in shape is increased by 25%. By what percent must the height be decreased so that there is no change in its volume?
- A. 10
- B. 25
- C. 36
- D. 50 (A.A.O. Exam, 2009)
Answer: 36
537. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by
- A. 0%
- B. 25%
- C. 62.5%
- D. 75%
Answer: 62.5%
538. The radius of a wire is decreased to one-third and its volume remains the same. The new length is how many times the original length?
- A. 1 time
- B. 3 times
- C. 6 times
- D. 9 times
Answer: 9 times
539. X and Y are two cylinders of the same height. The base of X has diameter that is half the diameter of the base of Y. If the height of X is doubled, the volume of X becomes
- A. equal to the volume of Y
- B. double the volume of Y
- C. half the volume of Y
- D. greater than the volume of Y
Answer: half the volume of Y
Explanation: Let the height of X and Y be h, and their radii be r and 2r respectively. Then, Volume of X = πr2h and Volume of Y = π (2r)2 h = 4πr2h. New height of X = 2h. So, new volume of X = 2 22 11 (2 ) 2 (4 ) (Volume of ). 22 π =π = π = × r h rh rh Y
540. If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio of their radii is
- A. 6: 3
- B. 5: 3
- C. 2 : 3 / 2: 3
- D. 3: 2
Answer: 3: 2
Explanation: Let their heights be 2h and 3h and radii be r and R re-spectively. Then, pr2(2h) = pR2(3h) ⇒ 2 2 33 i.e. 3 : 2. 2 2 rr R R =⇒ =
541. If the height of a cylinder is increased by 15 percent and the radius of its base is decreased by 10 percent then by what percent will its curved surface area change?
- A. 3.5 percent decrease
- B. 3.5 percent increase
- C. 5 percent decrease
- D. 5 percent increase
Answer: 3.5 percent increase
542. The radii of the bases of two cylinders are in the ratio 3 : 4 and their heights are in the ratio 4 : 3. The ratio of their volumes is
- A. 2 : 3 / 2: 3
- B. 3 : 2 / 3: 2
- C. 3 : 4 / 3: 4
- D. 4 : 3 / 4: 3
Answer: 3 : 4 / 3: 4
543. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio of the volume of the reduced cylinder to that of the original one?
- A. 1 : 2 / 1: 2
- B. 1 : 4 / 1: 4
- C. 1 : 8 / 1: 8
- D. 8 : 1 / 8: 1
Answer: 1 : 4 / 1: 4
544. The height of a closed cylinder of given volume and the minimum surface area is
- A. equal to its diameter
- B. half of its diameter
- C. double of its diameter
- D. None of these
Answer: equal to its diameter
545. The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
- A. 3 : 7 / 3: 7
- B. 7 : 3 / 7: 3
- C. 6 : 7 / 6: 7
- D. 7 : 6 / 7: 6
Answer: 7 : 3 / 7: 3
546. The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq. metres, its volume is
- A. 3180 m3
- B. 4620 m3
- C. 5240 m3
- D. None of these
Answer: 4620 m3
547. The radius of the cylinder is half its height and area of the inner part is 616 sq. cms. Approximately how many litres of milk can it contain?
- A. 1.4
- B. 1.53
- C. 1.7
- D. 1.9
Answer: 1.53
548. The diameter of the base of a cylindrical drum is 35 dm and the height is 24 dm. It is full of kerosene. How many tins each of size 25 cm × 22 cm × 35 cm can be filled with kerosene from the drum?
- A. 120
- B. 600
- C. 1020
- D. 1200
Answer: 1200
549. Two cans have the same height equal to 21 cm. One can is cylindrical, the diameter of whose base is 10 cm. The other can has square base of side 10 cm. What is the difference in their capacities?
- A. 250 cm3
- B. 300 cm3
- C. 350 cm3
- D. 450 cm3
Answer: 450 cm3
550. The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is
- A. 2 : 1 / 2: 1
- B. 3 : 2 / 3: 2
- C. 4 : 3 / 4: 3
- D. 5 : 3 / 5: 3
Answer: 4 : 3 / 4: 3
551. A closed metallic cylindrical box is 1.25 m high and its base radius is 35 cm. If the sheet metal costs ₹ 80 per m2, the cost of the material used in the box is
- A. ₹ 281.60
- B. ₹ 290
- C. ₹ 340.50
- D. ₹ 500
Answer: ₹ 281.60
552. The height of a right circular cylinder is 14 cm and its curved surface is 704 sq. cm. Then its volume is:
- A. 1408 cm3
- B. 2816 cm3
- C. 5632 cm3
- D. 9856 cm3
Answer: 2816 cm3
553. The radius and height of a cylinder are in the ratio 5 : 7 and its volume is 4400 cm3. Then its radius will be
- A. 4 cm
- B. 5 cm
- C. 10 cm
- D. 12 cm
Answer: 10 cm
554. A well has to be dug out that is to be 22.5 m deep and of diameter 7m. Find the cost of plastering the inner curved surface at ₹ 3 per sq. meter.
- A. ₹ 1465
- B. ₹ 1475
- C. ₹ 1485
- D. ₹ 1495
Answer: ₹ 1485
555. The volume of a right circular cylinder whose curved surface area is 2640 cm2 and circumference of its base is 66 cm, is
- A. 3465 cm3
- B. 7720 cm3
- C. 13860 cm3
- D. 55440 cm3
Answer: 13860 cm3
556. Three rectangles A1, A2 and A3 have the same area. Their lengths a1, a2 and a3 respectively are such that a1 < a2 <a3. Cylinders C1, C2 and C3 are formed from A1, A2 and A3 respectively by joining the parallel sides along the breadth. Then
- A. C1 will enclosed maximum volume
- B. C2 will enclosed maximum volume
- C. C3 will enclosed maximum volume
- D. Each of C1, C2 and C3 will enclose equal volume
Answer: C3 will enclosed maximum volume
Explanation: Let the breadths of the rectangles A1, A2 and A3 be b1, b2 and b3 respectively. Since the rectangles have the same area and a1 < a2 < a3, we have: b1 > b2 > b3. When the rectangles are folded to form cylinders, then their lengths a1, a2, a3 determine the radii of the cylinders while their breadths b1, b2, b3 form their heights. Volume of cylinder = pr2h. Clearly, the rectangle A3 with length a3 shall have maxi-mum value of r2 and hence C3 has maximum volume.
557. Two rectangular sheets of paper, each 30 cm × 18 cm are made into two right circular cylinders, one by rolling the paper along its length and the other along the breadth. The ratio of the volumes of the two cylinders, thus formed, is
- A. 2 : 1 / 2: 1
- B. 3 : 2 / 3: 2
- C. 4 : 3 / 4: 3
- D. 5 : 3 / 5: 3
Answer: 5 : 3 / 5: 3
558. Capacity of a cylindrical vessel is 25.872 litres. If the height of the cylinder is three times the radius of its base, what is the area of the base?
- A. 336 cm2
- B. 616 cm2
- C. 1232 cm2
- D. Cannot be determined
Answer: 616 cm2
559. The volume of a right circular cylinder, 14 cm in height is equal to that of a cube whose edge is 11 cm. The radius of the base of the cylinder is
- A. 5.2 cm
- B. 5.5 cm
- C. 11 cm
- D. 22 cm
Answer: 5.5 cm
560. The capacity of a cylindrical tank is 246.4 litres. If the height is 4 metres, what is the diameter of the base?
- A. 1.4 m
- B. 2.8 m
- C. 14 m
- D. 28 m
Answer: 28 m
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