Page 303 - Start Up Mathematics_8 (Non CCE)

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.
2
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

Thinking Skills

1. 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
2. The area of adjacent faces of a cuboid are x, y and z. Show that the volume of the cuboid is xyz.

3. If V is the volume of a cuboid of dimensions a × b × c and S is its surface area, then prove that
Ê
1 = 2 1 + 1 + 1ˆ .
˜
Á
Ë
V S a b c¯
4. 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.

Values and Life Skills

1. If the rainfall on a particular day was 6 cm, how many litres of water fell on a field of 2 hectares on that
day? How can rainwater be harvested?
2. The outer diameter of a pipe is 1 m and it is 21 m long, find:
(a) the outer curved surface area of the pipe.
2
(b) the cost of painting the outer surface of the pipe at the rate of ` 25 per m .
Why is it necessary to paint iron pipes?

Some NCERT Textbook Questions
1. A suitcase with measures 80 cm × 48 cm × 24 cm is to be converted with a trapaulin cloth. How many
metres of trapaulin of width 96 cm is required to cover 100 such suitcases?
2
2. The lateral surface area of a hollow cylinder is 4224 cm . It is cut along its height and formed a rectangular
sheet of width 33 cm. Find the perimeter of rectangular sheet?
3. Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.

295