Question

A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top If the height of the cone is h and the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is

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

Answer 1

Answer: (B)

$\frac{2h}{3}$

Let the height of the cylinder be H.
As the circular cylinder and cone have an exact fitting, the radius of the cone and cylinder will be same.

Given, Total volume of the solid = 3 $\times$ Volume of cone

$⟹$ Volume of cylinder + Volume of cone = 3 $\times$ Volume of cone

$⟹\pi r^{2}H+\frac{1}{3}\pi r^{2}h=3\left(\frac{1}{3}\pi r^{2}h\right)$

$⟹H+\frac{1}{3}h=h$

$H=\frac{2}{3}h$