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
$\pi\text{R}^2_1\text{H}_1=\frac{1}3{}\pi\big(\text{R}^2_1\big)\text{H}_2$
$\Rightarrow\frac{\text{H}_1}{\text{H}_2}=\frac{1}{3}$
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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