Question

A right circular cone has for its base a circle having the same radius as a given sphere. The volume of the cone is one-half that 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. $\frac{2}{1}$
• D. $\frac{2}{3}$

Answer 1

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

Given, radius of the sphere and cone are same.
Also, Volume of cone $=\frac{1}{2}\times$ Volume of sphere
$\frac{1}{3}\pi r^{2}h=\frac{1}{2}\times \frac{4}{3}\pi r^3$
$=>h=2r$
Hence, the required ratio of height to the radius is $2:1$