Question

The surface area of a solid sphere is increased by 21% without changing it's shape. Find the percentage increase in its:

I)radius

2) volume

Answer 1

Let the original and increased surface areas be A1 and A2.

A1­/A2 = (r1/r2)2

1.21A1­/A1 = (r2/r1)2

1.1 = r2/r1

∴ r2 = 1.1r1

∴ Increase percentage = (r2 – r1) / (r1) x 100 % = (1.1r1– r1)/ (r1) x 100 % = 10

Hence, the percentage increase in radius is 10 %

Let the original and increased volume be V1 and V2.

V1/V2 = (r1­/r2)3

V2/V1 = (11/10)3

= 1.331

∴ V2 = 1.331 V1

Increase % = (V2 – V1) / (V1) x 100 % = (1.331 V1 – V1) / V1 x 100 %

= 33.1%

Hence, the percentage increase in volume is 33.1 %