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%

 

  • Correct Answer
    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 = (Initial surface area = 6 sides x 100 = 600)

Correct Answer: -1%



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