A solid consists of a circular cylinder with an exact fitting rig… - Vidyadip

MCQ

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

A
$2\text{h}$
✓
$\frac{2\text{h}}{3}$
C
$\frac{3\text{h}}{2}$
D
$4\text{h}$

✓

Answer

Correct option: B.

$\frac{2\text{h}}{3}$

Let $r$ be the radius of the base of solid.
Clearly,
The volume of solid $= 3 \ \times $ volume of cone
Vol. of cone $+$ Vol. of cylinder $= 3$ Volume of cone
Vol. of cylinder $= 2$ Vol. of cone
$\pi\text{r}^2\text{x}=2\times\frac{1}{3}\pi\text{r}^2\text{h}$
$\text{x}=\frac{2}{3}\text{h}$
Thus,
The height of cylinder $=\frac{2}{3}\text{h}$

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