Page 251 - ICSE Math 8

4. A hollow cylindrical pipe open at both ends is made of 2 cm thick iron. If the internal diameter is 50 cm
and the length of the pipe is 140 cm, find the volume of iron in it.
5. A rectangular sheet of dimensions 33 cm × 24 cm is rolled into a cylinder so that the smaller side becomes
the height of the cylinder. Find the volume of the cylinder so formed.

6. Two right circular cylinders of equal volumes have their height in the ratio 4 : 9. Find the ratio of their
curved surface areas.

7. Two right circular cylinders of equal heights have their radii in the ratio 2 : 5. Find the ratio of their curved
surface area and the ratio of their volumes.

8. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between
the surface areas of the two solids.
3
9. A solid cubical block of fine wood costs ` 256 at ` 500 per m . Find the length of each side and its
volume.
10. A hollow garden roller which is 49 cm wide and has a
girth of 176 cm is made of 2 cm thick cast iron. Find the ¨ girth
3
volume of iron and weight of roller if 1 cm of iron weighs
7.5 grams.

[Hint: R Æ external radius, 2pR = 176] 49 cm
11. A wall 15 m long, 30 cm wide and 4 m high is made of bricks, each measuring 22 cm × 12 cm × 7.5 cm.
1
If of the total volume of the wall consists of mortar, how many bricks are there in the wall?
12
12. The area of adjacent faces of a cuboid are x, y and z. Show that the volume of the cuboid is xyz.

13. If V is the volume of a cuboid of dimensions a × b × c and S is its surface area, then prove that
1 = 2 1 + 1 + 1ˆ .
Ê
˜
Á
Ë
V S a b c¯
14. A circular wire of radius 42 cm is cut and bent in the form of a rectangle whose sides are in the ratio of
6 : 5. Find the smaller side of the rectangle.

THINK SMART

1. Find the length of the longest rod that can be placed in a room 12 m long, 9 m wide and 8 m high.
2. An adult requires 11 cubic metre of air in 24 hours. If there is 1331 cubic metre of air in a cubical room,
how many people can survive for 24 hours in that room?

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