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.
$1 : 3$
Let the height of a circular cylinder and a right circular cone be $h\ cm$ and $H\ cm$ respectively.
Since a right circular and a right circular cone have the same radius and the same volume,
$\Rightarrow\pi\text{r}^2\text{h}=\frac{1}{3}\pi\text{r}^2\text{H}$
$\Rightarrow\text{h}=\frac{1}{3}\text{H}$
$\Rightarrow\frac{\text{h}}{\text{H}}=\frac{1}{3}$
$⇒$ Ratio of the height is $1 : 3.$
Since a right circular and a right circular cone have the same radius and the same volume,
$\Rightarrow\pi\text{r}^2\text{h}=\frac{1}{3}\pi\text{r}^2\text{H}$
$\Rightarrow\text{h}=\frac{1}{3}\text{H}$
$\Rightarrow\frac{\text{h}}{\text{H}}=\frac{1}{3}$
$⇒$ Ratio of the height is $1 : 3.$
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