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:
- A3 : 5
- B3 : 1
- C1 : 3
- D2 : 5
✓
Answer
- 1 : 3
Solution:
Let r be the radius of cylinder and cone and volumes are equal and h1 and h2 be their have h2 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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