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Please answer the following essay question:
Suppose each dimension of a cube is increased. What happens to the surface area when each dimension is doubled, tripled or, quadrupled?

1 Answer

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Answer:

24s^2, 54s^2, 96s^2

Explanation:

Let s represent the initial side length of the cube. Then the area of each face of the cube is A = 6s^2 (recalling that the area of a square of side length s is s^2).

a) Now suppose we double the side length. The total area of the 6 faces of the cube will now be A = 6(2s)^2, or 24s^2 (a 24 times larger surface area),

b) tripled: A = 6(3s)^2 = 54x^2

c) quadrupled? A = 6(4s)^2 = 96s^2

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