A right circular cylinder and a right circular cone have the same… - Vidyadip

MCQ

A right circular cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is:

A
$3 : 5$
B
$2 : 5$
C
$3 : 1$
✓
$1 : 3$

✓

Answer

Correct option: D.

$1 : 3$

Volume of a right circular cylinder $=\pi\text{R}^2_1\text{H}_1=\text{v}_1$
Volume of a right circular cone $=\frac{1}3{}\pi\text{R}^2_2\text{H}_2=\text{v}_2$
If $V^1 = V^2$ and $R^1 = R^2,$ then
$\pi\text{R}^2_1\text{H}_1=\frac{1}3{}\pi\big(\text{R}^2_1\big)\text{H}_2$
$\Rightarrow\frac{\text{H}_1}{\text{H}_2}=\frac{1}{3}$

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