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The question is from CAT Percentages. CAT tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2019. This questions combines a bit of Geometry with Percentage. Percentages is an important topic for CAT. When the length, breadth and height of a cube changes by some percentage, what will be percentage change in surface area of the cube?

Question 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%

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Explanatory Answer

Method of solving this CAT Question from Percentages: How would change in length, breadth and height of a cube affect the surface area.

Let the surface area of each side of initial cube be 100.
The surface area of the resulting cuboid would be given by 2(lb + bh + lh)
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 * (−6/600) ∗ 100 = −1 (Initial surface area = 6 sides x 100 = 600)

The question is "What is the percentage change in surface area of this cube?"
The percentage change in surface area of this cube is -1%.

Hence, the answer is -1%.

Choice D is the correct answer.

 

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