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Question
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?
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Solution
Surface area of a cube = 6a2, where a is side of a cube.
... Side of cube = 5 cm
... Surface area of the cube = 6 × (5)2 = 6 × 25 = 150 cm2
Now, surface area of the cube with side 1 cm = 6 × (1)2 = 6 cm2
... Surface area of 5 cubes with side 1 cm = 5 × 6 = 30 cm2
Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes
= `30/150`
= `3/15`
= 1 : 5
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