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Question

Each side of a cube is increased by 50%. Then the surface area of the cube is increased by:

A
50%
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B
100%
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C
125%
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D
150%
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Solution

The correct option is C 125%
Let original side be L units in length.
New side length = 1.5L (after increase).
Original surface area = 6×L2
Increased surface area = 6×(1.5L)2=13.5L2
Then, % increase in surface area
=Increased surface areaOriginal surface areaOriginal surface area×100

=13.5L26L26L2×100=125%

[Alternate method:
Let the edge be a cm.
New edge (after increase)
=a+50%a=a+a2=3a2

TSA of the original cube =6a2

TSA of new cube
=6×(3a2)2=6×9a24=2.25×6a2

Increase in area =[2.25×6a2][6a2]=(2.251)×6a2=1.25×6a2=1.25×TSA of the original cube

Increase %=125%]

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