The radius of a sphere is equal to the radius of the base of a right circular cone and the volume of...........

Quantitative Aptitude (CDS) Mensuration 3D

The radius of a sphere is equal to the radius of the base of a right circular cone, and the volume of the sphere is double the volume of the cone. The ratio of the height of the cone to the radius of its base is

2 :1

1 : 2

2 : 3

3 : 2

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Explanation:

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 $\pi$ R³= 2 x 1/3 x r²x h
=> 2r³ =r²h
=>h/r =2
Thus, the ratio of the height of the cone to radius of its base is 2:1.