Question

If the radius of a sphere is increases by 150% then percentage increase in volume is

• A. 100%
• B. 25%
• C. 125%
• D. $337\frac{1}{2}$%

Answer 1

Answer: (D)

$337\frac{1}{2}$%

Volume of a sphere of radius 'r' $=\frac{4}{3}\pi r^3$
New radius $=\frac{150}{100}r=\frac{3}{2}r$
Hence,

volume of the new sphere $=\frac{4}{3}\pi {\left(\frac{3}{2}r\right)}^3=\frac{27}{8}\times \frac{4}{3}\pi r^3$

Increase in volume $=\frac{NewVolume}{OldVolume}\times 100=\frac{\frac{27}{8}\times \frac{4}{3}\pi r^3}{\frac{4}{3}\pi r^3}\times 100=\frac{27}{8}\times 100=337\frac{1}{2}$ %