a) 2 : 1
b) 1 : 2
c) 2 : 3
d) 3 : 2
Answer: a
Explanation: Let the radius of cone and the sphere be R and the height of the cone be H
Volume of sphere $$ = \frac{4}{3}\pi {r^3}$$
Volume of cone $$ = \frac{1}{3}\pi {r^2}h$$
$$\eqalign{
& \Rightarrow \frac{4}{3}\pi {R^3} = 2 \times \frac{1}{3}\pi {R^2}H \cr
& \Rightarrow 4R = 2H \cr
& \Rightarrow \frac{H}{R} = \frac{4}{2}\,Or\,2:1 \cr} $$
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