# CAT Practice : Percents, Profits

Percentage Change in Surface Area

## Number of Students

Q.26: A solid cube made of steel is melted and recast such that its length, breadth and height changes as +10%, +10%, -20%. What is the percentage change in surface area of this cube?
1. No change
2. +1%
3. -2%
4. -1%

Choice D. -1%

## Detailed Solution

The surface area of the resulting cuboid would be given by 2(lb + bh + lh)

Let the surface area of each side of initial cube be 100

So, ∆lb = 100 + 10% ---> 110 + 10% ---> 121

∆bh = 100 + 10% ---> 110 - 20% ---> 88

∆lh = 100 + 10% ---> 110 - 20% ---> 88

Therefore, new surface area = 2 (121 + 88 + 88) = 594

% change in surface area = $a * \frac{-6}{600} * 100 = -1%$(Initial surface area = 6 sides x 100 = 600)

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