Page 304 - Start Up Mathematics_8 (Non CCE)

4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed
in the given cuboid?
5. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?
6. Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir
3
is 108 m , find the number of hours it will take to fill the reservoir.

Exemplar Problems

1. If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be:
(a) tripled (b) constant (c) one-sixth (d) one-third
2. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood as
2.5 cm. The volume of the wood is:
3
3
3
(a) 85,000 cm (b) 80,000 cm (c) 82,125 cm (d) 84,000 cm 3
3. If a cube fits exactly in a cylinder with height h, then the volume of the cube is _________ and surface
area of the cube is ___________.
4. Two cylinders of same volume have their radii in the ratio 1:6, then ratio of their heights is ___________.
5. The surface area of a cuboid formed by joining face to face 3 cubes of side x is 3 times the surface area
of a cube of side x. (True/False)
6. A river 2 m deep and 45 m wide is flowing at the rate of 3 km per hour. Find the amount of water in cubic
metres that runs into the sea per minute.

Quizzes

1. A cube of side 3 cm is cut into smaller cubes of side 1 cm each. If the original cube was
painted black on all sides, then how many smaller cubes do not have any paint?

2. A cuboid of dimensions 12 cm × 10 cm × 8 cm
was painted magenta, yellow and grey on opposite Magenta
faces. It was cut into cubical blocks each of side
2 cm. Yellow
(a) What is the number of cubes obtained? Grey

(b) What is the number of cubes with only
one face painted?

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