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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