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$3 : 1$
- ✓$1 : 3$
- D$2 : 5$
✓
Answer
Correct option: C.
$1 : 3$
Let $r$ be the radius of cylinder and cone and volumes are equal and $h_1$ and $h_2$ be their have $h_2$ is respectively
$\therefore$ Volume of cylinder $=\pi\text{rh}_1$
and volume of cone $=\frac{1}{3\pi\text{r}^2\text{h}_2}$
$\therefore\pi\text{r}^2\text{h}_1=\frac{1}{3\pi\text{r}^2\text{h}_2}$
$\Rightarrow\text{h}_1=\frac{1}{3\text{h}_2}$
$\Rightarrow\frac{\text{h}_1}{\text{h}_2}=\frac{1}{3}$
$\therefore\text{h}_1:\text{h}_2=1:3$
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