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What is the surface area of the new cuboid if each edge of a cuboid with surface area S is doubled?

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2 S

4 S

6 S

8 S

answer is B.

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Detailed Solution

Given that, each edge of the cuboid is doubled.
We have to find the surface area of the new cuboid.
Surface area of the first cuboid with length l, breadth b and height h is,

S = 2 (l b + b h + h l)

We will use this formula to find the new surface area in which each edge is doubled, that, 2l, 2b, 2h, then,

S' = 2 [(2 l) (2 b) + (2 b) (2 h) + (2 h) (2 l)]

⇒ S' = 2 (4 l b + 4 b h + 4 h l)

⇒ S' = 4 [2 (l b + b h + h l)]

⇒ S' = 4 S

Thus, the new surface area is 4 times the old surface area.
Hence, option 2 is the correct option.

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