with the view to crack tier -2, we shared very important topic for CGL - Prism and Cylinder, go through all the these questions and build your confidence.
Prism and Cylinder
1.The base of a prism is a triangle of which the sides are 17 cm, 25 cm and 28 cm
respectively. The volume of the prism is 4200 cubic cm. What is the height? Find its lateral area also?
2. There are two prisms, one has equilateral triangle as a base and the other a regular
hexagon. If both of the prisms have equal heights and volumes, then find the ratio
between the length of each side at their bases?
3. A well with 7 metres inside diameter is dug 22.5 metres deep. Earth taken out of it is
spread all round to a width of 10.5 metres to form an embankment. Find the height of
embankment? (Take pi = 22/7)
4. A cylindrical tank of diameter 35 cm is full of water. If 11 litres water is taken out from the tank, find the drop in the water level in the tank?
(Use pi = 22/7)
5. Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 7 metres per second into a cylindrical tank the radius of whose base is 40 cm. By how much will the level of water rise in half an hour?
6. Into a circular drum of radius 4.2 m and height 3.5 m, how many full bags of wheat can be emptied if the space required for wheat in each bag is 2.1 cubic m.
(use pi = 22/7)
7. How many cubic metres of earth must be dugout to sink a well 22.5 m deep and of diameter 7 m? Also, find the cost of plastering the inner curved surface at Rs 3 per square metre ?
8. The diameters of the internal and external surface of a hollow spherical shell are 6 cm
and 10 cm respectively. If it is melted and recast into a solid cylinder of height 3
2 2 cm find the diameter of the cylinder?
(Take pi = 22/7)
9. A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of
diameter 3.5 cm through which water flows at the rate of 2 m/s. Calculate in minutes the
time it takes to fill the tank?
(Use pi = 22/7)
10. Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical holes have
been made from its both ends. If the diameter of the hole is 6 cm and height 4 cm, find
(i) Volume of the cylinder?
(ii) Volume of one conical hole?
(iii) Volume of the remaining solid?
11. A milk tanker cylindrical in shape having diameter 2 metres and length 4.2 metres
supplies milk to the two booths in the ratio 3 : 2. One of the milk booths has a rectangular vessel having base areas 3.96 sq m and the other has a cylindrical vessel having diameter 2 metres. Find the level of milk in each of the two vessels?
12. Two cylindrical vessels are filled with oil. The radius of one vessel is 15 cm and its
height is 25 cm. The radius and height of the other vessel are 10 cm and 18 cm
respectively. Find the radius of a cylindrical vessel 30 cm in height, which will just
contain the oil of the two given vessels.
13. The radius of the base of a right circular cone is 14 cm and altitude 20 cm. What is the largest lateral surface area possible for a cylinder inscribed in this cone?
14. The thickness of a metallic tube is 1 cm and the inner diameter of the tube is 12 cm. Find the weight of 1 m long tube, if the density of the metal be 7.8 gm per cm3.
15. A cylindrical road roller made of iron is 1 m wide. Its inner diameter is 54 cm and
thickness of the iron sheet rolled into the road roller is 9 cm. Find the weight of the
roller if 1 cc of iron weighs 8 gm.
16. The volume of a metallic cylindrical pipe is 748 cm3. Its length is 14 cm and its external radius is 9 cm. Find its thickness?
17. Increasing the radius of the base of cylinder by 6 units increase the volume by y cubic units. Increasing the altitude of the cylinder by 6 units also increase the volume by y cubic units. If the original altitude is 2 units, find the original radius?
18. The depth of the water in a rectangular swimming pool increases uniformly from 1
metre at the shallow end to 3.5 metres at the deep end. The pool is 25 metres long and 12 metres wide. Calculate the volume of the water in the pool in cubic metres. The pool is emptied by means of cylindrical pipe of internal radius 9 cm. The water flows down the pipe at a speed of 3 metres per second. Calculate the number of litres emptied from the pool in 1 minute giving your answer to the nearest 10 litres.
(1 litres = 1000 cm3).
(Take pi = 3.142)
19. The total surface area of a right triangular prism of the height 4 cm is 72 √3 cm2. If the base of the prism is an equilateral triangle, find its volume?
20. The sum of radius of the base and height of a right circular cylinder is 37 cm. If the total surface area of the cylinder is 1628 cm2, find its volume.
(Use pi = 22/7)
21. 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 raise by 7 cm.
(Use pi = 22/7)
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