Question

The volume of a cone is equal to that of a sphere. If the diameter of the base of cone is equal to the diameter of the sphere, what is the ratio of the height of the cone to the diameter of the sphere

• A. $2:1$
• B. $1:2$
• C. $3:1$
• D. $4:1$

Answer 1

The correct option is A $2:1$

Let R be a radius of a sphere, h and r are height and radius of cone respectively.

Given: Diameter of base of cone= Diameter of sphere

$d=D\Rightarrow r=R$

Now volumes are equal,

$\therefore \frac{1}{3}\pi r^{2}h=\frac{4}{3}\pi R^3$

Cancelling $3,\pi ,r$&$R$

$\therefore h=4R$

$\Rightarrow h=4\frac{D}{2}$

$\Rightarrow h=2D$

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

Thus, $h:D=2:1$