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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?

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(i) Let initially the edge of the cube be l. Initial surface area = 6l2

If each edge of the cube is doubled, then it becomes 2l.

New surface area = 6(2l)2 = 24l2 = 4 × 6l2

Clearly, the surface area will be increased by 4 times.

(ii) Initial volume of the cube = l3

When each edge of the cube is doubled, it becomes 2l.

New volume = (2l)3 = 8l3 = 8 × l3

Clearly, the volume of the cube will be increased by 8 times.

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