Question

The height and base radius of a cone are each increased by 100% then the volume of the cone becomes

• A. double
• B. three times
• C. six times
• D. eight times

Answer 1

Answer: (D)

eight times

Let the base radius and height of cone is r and h respt.

Then volume =$\frac{1}{3}\pi r^{2}h$ cu cm

If Base radius increased 100% new radius =$r\times \frac{200}{100}=2r$ cm

If Base height increased 100% new height =$h\times \frac{200}{100}=2h$ cm

So volume of new cone =$\frac{1}{3}\left(2r{)}^2\right(2h)=\frac{1}{3}\times (4r^2)\times (2h)=\frac{8}{3}\pi r^{2}h$ cu cm

Then ratio of new and old volume=$\frac{\frac{8\pi r^{2}h}{3}}{\frac{\pi r^{2}h}{3}}=8$