Question

A right circular cone having a circular base and same radius as that of a given sphere. The volume of the cone is one half of the sphere. The ratio of the altitude of the cone to the radius of its base is:

• A. $\frac{1}{1}$
• B. $\frac{1}{2}$
• C. $\frac{2}{3}$
• D. $\frac{2}{1}$
• E. $\sqrt{\frac{5}{4}}$

Answer 1

The correct option is D $\frac{2}{1}$

Let the radius of cone be $r$ and height be $h$

Volume of right circular cone =$\frac{1}{3}\pi r^{2}h$

Given volume of right circular cone is half of the volume of sphere

$\Rightarrow \frac{1}{3}\pi r^{2}h=\frac{1}{2}\times \frac{4}{3}\pi r^3$

$\Rightarrow \frac{h}{r}=2$