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Total Surface Area of a cube

If each edge ...

Question

If each edge of a cube of surface area $^{'} S^{'}$ is doubled, then the surface area of the new cube is

A

2 S

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B

4 S

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C

6 S

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D

8 S

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Solution

The correct option is D: $4 S$
Let each edge of a cube $= a$

Then surface area $= 6 a^{2}$

$∴ S = 6 a^{2}$

Now doubling the edge, we get
New edge of the new cube $= 2 a$

$∴$ New Surface area $= 6 (2 a)^{2}$

$= 6 \times 4 a^{2} = 24 a^{2}$

$= 4 \times 6 a^{2} = 4 S$

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