Page 238 - ICSE Math 8

Example 2: 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
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Volume of cube = (Side) = (8) = 8 × 8 × 8 = 512 cm 3
Side of small cube = 2 cm
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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 3: 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.
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Volume of cube = x cm fi x = 1,728 fi x = 1 728, = 12
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\ Edge of the cube = 12 cm
Example 4: A rectangular block of ice measures 40 cm by 25 cm by 15 cm. Calculate its weight in kg, if
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ice weighs of the weight of the same volume of water and 1 cm of water weighs 1 g.
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Solution: Volume of rectangular block of ice = 40 cm × 25 cm × 15 cm = 15,000 cm 3
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Now, weight of 1 cm of water = 1 g and, weight of 1 cm of ice = Ê Á 9 ˆ ˜ th of the weight of
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1 cm of water Ë 10¯
9 ˆ
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\ Weight of 1 cm of ice = Ê 10¯ g
Á
˜
Ë
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\ Weight of rectangular block of ice = × 15 000, g = 13,500 g = 13.5 kg
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Example 5: 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

Volume of box
\ Number of soap cakes that can be put in the box =
Volume of 1soap cake
12 60 000, ,
= = 31,500
40
Example 6: Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of
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the reservoir is 108 m , find the number of hours it will take to fill the reservoir.
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Solution: Volume of reservoir = 108 m = (108 × 1,000) L = 1,08,000 L ( 1 m = 1,000 L)
Rate of pouring of water = 60 litres/minute

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