Question

The volume of a cylinder becomes $—$ the original volume if its radius becomes half the original radius .

Answer 1

We know that volume of cylinder is $={\text{πr}}^2\text{h}$

Where $\text{h}$ is the height of cylinder and $\text{r}$ is the radius of the cylinder .

Now if the radius becomes half then $\text{r=}\frac{\text{r}}{2}$

We put the value of $\text{r}$ in the formula and we get

Volume of cylinder $=\mathrm{\pi }{\left(\frac{\text{r}}{2}\right)}^2\mathrm{h}=\frac{{\text{πr}}^2\text{h}}{4}=\frac{1}{4}(\mathrm{\pi }{\text{r}}^2\text{h)}$$=\frac{1}{4}$(original Volume)

Hence volume of the cylinder becomes $\frac{1}{4}$ times the original volume .