Question

If each edge of a cube is increased by 50 percent then by what percentage its surface area & volume increased?

Answer 1

Let the original length of the edge = x

The length of the length after 50% increase is 1.5x

Find the original surface area:

Area = 6 x side²

Area = 6 x²

Find the increased in surface area:

Area = 6 x side²

Area = 6 (1.5x)²

Area = 13.5 x²

Find the increased in area:

Percentage increase =  new area / original area x 100

Percentage increase =  (13.5x² /6x² ) x 100  = 225%

Find the original volume:

Volume = Length³

Volume = x³

Find the new volume:

Volume = Length³

Volume = (1.5x)³ = 3.375 x³

Find the increased in volume:

Percentage increased = (3.375x³ ÷ x³) x 100 = 337.5%

Answer: The surface area is increased by 225% and the volume is increased by 337.5%

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SHORT CUT:

Increased in area = (increased in length)²

Increased in area = (1.5)²

Increased in area = 2.25 times or 225%

Increased in volume = (increased in length)³

Increased in area = (1.5)³

Increased in area = 3.375 times or 337.5%