Sheet MENSURATION – 3D
07
– 3D
9. The radius of two circular cylinders are in the ratio 14. The height of a circular cylinder is increased six times
3 : 2 and the ratio of their volumes is 27 : 16. What and the base area is decreased to one ninth of its
is the ratio of their heights?/ value. The factor by which the lateral surface of the
cylinder increases is:
(a) 8 : 9 (b) 3 : 4 (c) 4 : 3 (d) 9 : 8
1
9
10. The ratio of the volume of first and second cylin-
der is 32 : 9 and the ratio of their heights is 8 : 9. If
the area of the base of the second cylinder is 616 1 2 3
(a) 2 (b) (c) (d)
cm², then what will be the radius of the first cyl- 2 3 2
inder?/ 15. The diameter of a 120 cm long roller is 84 cm. It
takes 500 complete revolutions of the roller to level
a ground. The cost of leveling the ground at Rs.
cm²
1.50 sq. m. is:
(a) 24 cm (b) 20 cm (c) 28 cm (d) 36 cm cm cm
11. The ratio of curved surface area and volume of a
cylinder is 1 : 7. The ratio of total surface area and
volume is 187 : 770. What is the respectively ratio
of its base radius and height?
(a) 5750 (b) 6000 (c) 3760 (d) 2376
16. A field roller, in the shape of a cylinder, has a di-
1
ameter of 1 m and length of 1 m. If the speed at
4
(a) 5 : 8 (b) 4 : 9 (c) 3 : 7 (d) 7 : 10 which the roller rolls is 14 revolutions per minute,
then the maximum area (in m²) that it can roll in 1
12. The radius and height of a solid cylinder are in-
creased by 2% each, What will be the approxi- hour is. /
mate percentage increase in volume?/ 1
1
4
2
22
(a) 6.76 (b) 5.88 (c) 6.12 (d) 3.34 π=
7
13. If the radius of the base of a right circular cylinder
(a) 3560 (b) 3300 (c) 3600 (d) 3960
is increased by 20% and the height is decreased
by 30%, then what is the percentage increase/ 17. The radius of a cylinder is 10 cm and its height is
decrease in the volume? 4 cm. How much cm does we add either in radius
or in height to get the same change in the volume?
(a) Dec. 0.8% (b) Inc. 2%
(c) Inc. 0.8% (d) Dec. 2% (a) 4 (b) 5 (c) 6 (d) 7
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18. How many smaller cylinder of height & radius 3.5 23. A 15 m deep with radius 2.8 m is dug and the
cm can be made from a larger cylinder of height 14 earth taken out taken out from it is spread evenly
cm and radius 7 cm ?/ to form a platform of breadth 8 m and height 1.5
m. What will be the length of the platform?/
(a) 36 (b) 25 (c) 16 (d) 4
19. Find the weight of a cylindrical iron container with
base radius 12.6 cm and height is 4 m. where the
weight of 1 cm³ of iron is 2 grams? / cm (a) 28.8 m (b) 30.8 m
m (c) 28.4 m (d) 30.2 m
1 cm³ 24. A cylinder of maximum volume is cut out of a solid
wooden cube. How much solid is wasted in this
(a) 299.284 kg (b) 199. 584 kg
process (in %)?/
(c) 399. 168 kg (d) 499.482 kg
20. A patient in a hospital is given tea daily in a cylin-
drical cup of diameter 7 cm. If the cup is filled with
tea to a height of 4 cm, how much tea the hospital (a) 26.31% (b) 20.56%
has to prepare daily to serve 180 patients?/
(c) 24.67% (d) 21.42%
25. 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 sec-
22 ond cylinder?
π=
7
(a) 22.77 litres (b) 27.27 litres
(c) 22.27 litres (d) 27.72 litres
21. Two rectangle sheets of paper each 30 cm × 18 cm
(a) 5 (b) 6 (c) 15 (d) 7.5
are made into two right circular cylinders, one by
rolling the paper along its length and the other 26. Find the length of the string wound on a cylinder
along the breadth. The ratio of the volumes of the 1
two cylinders thus formed is. tank whose base diameter and height are 5 cm
11
× and 48 cm respectively. The string makes exactly
4 complete turns around the cylinder while it is
two ends touch the top and bottom of the tank ?
1
5
11
(a) 2 : 1 (b) 3 : 5 (c) 4 : 3 (d) 5 : 3
22. A cylindrical vessel of radius 30 cm and height 42
cm is full of water. Its contents are emptied into a
rectangular tub of length 75 cm and breadth 44
cm. The height to which the water rises in the tub (a) 70 cm (b) 80 cm
is ?/ (c) 90 cm (d) 100 cm
(a) 36 (b) 30 (c) 40 (d) 45
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