The radius of the base of a right cylinder is halved, keeping the height same. What is the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder?

# The radius of the base of a right cylinder is halved, keeping the height same. What is the ratio of the volume of the cylinder thus obtained to the volume of the original cylinder?

1. A
1:4
2. B
2:9
3. C
6:8
4. D
7:9

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### Solution:

Let radius and height be r and h
$⇒$Volume of cylinder = $\pi {r}^{2}h$
$⇒$radius of new cylinder = $\frac{r}{2}$        ……..(given)
$⇒$Volume of new cylinder = $\pi {\left(\frac{r}{2}\right)}^{2}h$ = $\frac{\pi {r}^{2}h}{4}$
$⇒\frac{\mathit{Volume of new cylinder}}{\mathit{Volume of original cylinder}}$ = $\frac{\frac{\pi {r}^{2}h}{4}}{\pi {r}^{2}h}$ = $\frac{1}{4}$
Hence, the ratio is 1:4

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