Class 9
Mensuration Practice Set
2. Calculate the edge of the cube if its volume is 1331 cm3.
3. Find the area of the sheet required to make closed cylindrical vessel of height 1 m and diameter 140 cm.
4. How many balls, each of radius 2 cm can be made from a solid sphere of lead of radius 8 cm ?
5. In a cylinder, if radius is halved and height is doubled, then find the volume with respect to original volume.
6. The curved surface area of a cylinder is 176 cm2 and its area of the base is 38.5 cm2. Find the volume of the cylinder.
7. The diameter of a roller is 42 cm and its length is 120 cm. It takes 500 complete revolutions to move once to land a playground. Find the area of the playground in m².
8. The curved surface area of a cylinder is 154 cm2. The total surface area of the cylinder is three times its curved surface area. Find the volume of the cylinder.
9. How many metres of 5 m wide cloth will be required to make a conical tent, the radius of whose base is 3.5 m and height is 12 m ?
10. How many metres of 5 m wide cloth will be required to make a conical tent, the radius of whose base is 3.5 m and height is 12 m ?
11. A tent is in shape of a right circular cylinder up to a height of 3 m and a cone above it. The maximum height of the tent above ground is 13.5 m. Calculate the cost of painting the inner side of the tent at the rate of Rs 3 per sq. m, if the radius of the base is 14 m.
12. Manoj Sweets placed an order of making 30 cm x 20 cm x 6 cm cardboard boxes for packing their sweets. For all overlaps, 5 % of total area is required extra. If cost of the cardboard is Rs 2 for 1000 cm2 , find the cost of the cardboard used for making 500 boxes.
13. A metallic right circular cylinder is 15 cm high and the diameter of its base is 14 cm. It is melted and recasted into another cylinder with radius 4 cm. Find its height and curved surface area of the new cylinder.
14. A spherical ball is divided into two equal halves. If the curved surface area of each half is 56.57 cm, find the volume of the spherical ball. [use π = 3.14]
15. A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find it volume. If 1m3 wheat cost is ₹10, then find total cost.
16. A wall of length 10 m is to be built across an open ground. The height of the wall is 5 m and thickness of the wall is 42 cm. If this wall is to be built with brick of dimensions 42 cm × 12 cm × 10 cm, then how many bricks would be required?
17. A right triangle of hypotenuse 13 cm and one of its sides 12 cm is made to revolve taking side 12 cm as its axis. Find the volume and curved surface area of the solid so formed.
18. Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.
19. A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 6 cm and its height is 4 cm. Find the cost of painting the toy at the rate of Rs. 5 per 1000 cm2.
20. If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?
21. A solid cylinder has a total surface area of 213 cm2. Its curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.
22. The dimensions of a cuboid are in the ratio 1: 2: 3 and its total surface area is 88 m2. Find the dimensions.
23. A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm3. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use π = 3.14)
24. A well of diameter 4 m is dug 14 m deep. The earth taken out is spread evenly all around the well to form a 40 cm high embankment. Find the width of the embankment.
25. Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm.
26. A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of 10 per 100 cm2.
27. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder. (Use π = 22/7)
28. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total (inner) suface area of the vessel.
29. Prove that volume of sphere is equal to 4/3 pi.
~Seminary Classes
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