the radius of a sphere is increased by 50 increase in..., Area & Volume, General Mathematics

Question:The radius of a sphere is increased by `50%`. The increase in the surface area of the sphere is :

A `100%` 
B `125%` 
C `150%` 
D None

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+ AnswerD

+ ExplanationLet original radius = R.

Then, original volume 

`= 4/3 π R^3 = v (say)`

New volume 

`= 150/100 R`

`= 3/2 R.`

New volume 

`= 4/3 π (3/2 R)^3`

`= (4/3 π R^3). 27/8`

`27/ 8 V.`

Increase %

`= (19/8 V xx 1/V xxx 100)%`

`= 237.5%.`

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