UPSC 2015 CDS I Math Paper

Let r and h be the radius and height of the cone, respectively.
Suppose R is the radius of the sphere
R = r  (Given)
Volume of the sphere = 2 × Volume of the cone
∴‌‌

4

3

πR3=2×‌‌

1

3

π×r2×h
⇒2r3=r2h
⇒

h

r

=2
Thus, the ratio of the height of the cone to radius of its base is 2:1.