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?
Answers
1 % Reduction in surface area of cube if cube is melted & recasted such that Length breadth & height changes +10% , + 10% , -20% respectively
Step-by-step explanation:
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
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