Question

Question 5

If the height of a cylinder becomes $\frac{1}{4}$ of the original height and the radius is doubled, then which of the following will be true ?
(a) Volume of the cylinder will be doubled
(b) Volume of the cylinder will remain unchanged
(c) Volume of the cylinder will be halved
(d) Volume of the cylinder will be $\frac{1}{4}$ of the original volume

Answer 1

We know that the volume of a cylinder having base radius r and height h is $V=\pi r^{2}h$
Now, if new height is $\frac{1}{4}th$ of the original height and the radius is doubled. i.e.
$h^{\prime }=\frac{1}{4}hand{r}^{\prime }=2r,then$
New volume, $V^{\prime }=\pi (2r{)}^2\times \frac{1}{4}h=4\pi r^2\times \frac{1}{4}h$
$\pi r^{2}h=V$
Hence, the new volume of cylinder is same as the original volume.