Question

A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone, then the height of the cylinder is

• A. $2h$
• B. $4h$
• C. $\frac{2h}{3}$
• D. $\frac{3h}{2}$

Answer 1

The correct option is C $\frac{2h}{3}$

Let $h_1$, be height of cylinder and r be the radius of the cone and cylinder
Volume of the solid = 3 $\times$ Volume of cone

$\frac{1}{3}\pi r^{3}h+\pi r^2{h}_1=3.\frac{1}{3}\pi r^{2}h$
$Or\frac{1}{3}h+h_1=h$
$\Rightarrow h_1=\frac{2}{3}h$