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If a cube's edges are each increased by 50%, the percentage increase in the cube's surface area is

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50%

75%

100%

125%

answer is D.

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Detailed Solution

It is given that a cube's edges are each increased by 50%.
If

a

is the side length of a cube, then its total surface area is

6 a 2 .

Let the original side be

a .

Since the side of the new cube is increased by 50%, therefore, its side length will be,

a 100 + 50 100 = 3 a 2 .

Therefore, the new surface area of the cube can be calculated as,

S 1 = 6 3 a 2 2 ⇒ S 1 = 6 × 9 a 2 4 ⇒ S 1 = 27 a 2 2

An increase in the surface area is,

= 27 a 2 2 − 6 a 2 = 27 − 12 a 2 2

= 15 a 2 2

Therefore the increased surface percentage can be calculated as,

increase % = increase in surface area original surface area × 100 = 15 a 2 2 6 a 2 × 100 = 15 × 100 12 = 125 %

Therefore if a cube's edges are each increased by 50%, its surface area is increased by 125%.
Hence, option (4) is correct.

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