Question
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?
CAT 2021
Solution
Correct option is
(D)
Explanatory Answer :
Cube has all Sides Equal => Length = Breadth = Height = X Surface Area of Cube = 6X²
After melting & recasting Length = Breadth = X + (10/100)X = 1.1X Height = X - (20/100)X = 0.8X
Surface Area = 2( LB + BH + LH) = 2 ( 1.1X * 1.1X + 1.1X*0.8X + 1.1X*0.8X) = 2 * 1.1X² ( 1.1 + 0.8 + 0.8) = 2.2 X² * 2.7 = 5.94X²
Reduction in surface Area = 6X² - 5.94X² = 0.06X² percentage Reduction in surface area of this cube = (0.06X²/6X²) * 100 = 1 %
1 % Reduction in surface area of cube
