Page 284 - Start Up Mathematics_8 (Non CCE)

Solution: Length (l) = 10 cm + 10 cm = 20 cm, breadth (b) = 10 cm, height (h) = 10 cm

Volume = l × b × h
= 20 cm × 10 cm × 10 cm = 2,000 cm 3
Example 5: A cube of side 8 cm is cut into a number of cubes of side 2 cm each. Find the number of
cubes cut from the given cube.
Solution: Side of the given cube = 8 cm
3
3
Volume of cube = (Side) = (8) = 8 × 8 × 8 = 512 cm 3
Side of small cube = 2 cm
3
Volume of each small cube = (2) = 2 × 2 × 2 = 8 cm 3
Volume of bigcube 512
\ Number of small cubes = = = 64
Volume of smallcube 8

Example 6: A cuboid of dimension 18 cm × 16 cm × 6 cm is melted to form a cube. Find the edge of the
cube so formed.
Solution: Dimensions of cuboid = 18 cm, 16 cm, 6 cm
\ Volume of cuboid = 18 cm × 16 cm × 6 cm = 1,728 cm 3
Let the edge of the cube formed be x cm.

3
Volume of cube = x cm 3
3
fi x = 1,728 fi x = 1 728, = 12
3
\ Edge of the cube = 12 cm
Example 7: A rectangular block of ice measures 40 cm by 25 cm by 15 cm. Calculate its weight in kg,
9
3
if ice weighs of the weight of the same volume of water and 1 cm of water weighs
1 g. 10

Solution: Volume of rectangular block of ice = 40 cm × 25 cm × 15 cm = 15,000 cm 3
9 ˆ
3
3
Now, weight of 1 cm of water = 1 g and, weight of 1 cm of ice = Ê Á Ë 10¯ th of the weight of
˜
3
1 cm of water
Ê 9 ˆ
3
\ Weight of 1 cm of ice = Á 10¯ g
˜
Ë
9
\ Weight of rectangular block of ice = ¥ 15 000, g = 13,500 g = 13.5 kg
10
Example 8: A box is 2 m long, 90 cm wide and 70 cm high. How many soap cakes can be put in it if
each cake measures 5 cm by 4 cm by 20 mm?
Solution: Length of box (l) = 2 m = (2 × 100) cm = 200 cm
Width of box (b) = 90 cm, Height of box (h) = 70 cm
\ Volume of box = 200 cm × 90 cm × 70 cm = 12,60,000 cm 3

Length of soap cake = 5 cm, Width of soap cake = 4 cm
Ê 20ˆ
Height of soap cake = 20 mm = Á 10 ¯ cm = 2 cm
˜
Ë
\ Volume of 1 soap cake = 5 cm × 4 cm × 2 cm = 40 cm 3

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