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Question

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

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Solution

Let edge of given cube be a.

Volume of the cube, V=a3

and surface area, S.A=6a2

By doubling the edge of cube, the side of new cube =a×2=2a

New Volume =V=(2a)3=8a3=8×a3

and, New surface area, S.A=6(2a)2=6×4a2

=24a2=4×6a2

It is clear from the above that

V=8×V

and, S.A=4×S.A

Hence, Volume is increased 8 times and the surface area is 4 times.


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