Question

Q3.If the radius of a cylinder is doubled and height is halved,the volume will be double.State true or false and justify your answer.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{base}\mathrm{of}\mathrm{cylinder}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{its}\mathrm{height}. \\ \mathrm{Now},\mathrm{volume}\mathrm{of}\mathrm{cylinder}={\mathrm{\pi r}}^2\mathrm{h} \\ \mathrm{Now},\mathrm{new}\mathrm{radius}=\mathrm{R}=2\mathrm{r} \\ \mathrm{new}\mathrm{height},\mathrm{H}=\frac{\mathrm{h}}{2} \\ \mathrm{New}\mathrm{volume}={\mathrm{\pi R}}^2\mathrm{H}=\mathrm{\pi }{\left(2\mathrm{r}\right)}^2\left(\frac{\mathrm{h}}{2}\right)=2{\mathrm{\pi r}}^2\mathrm{h}=2\times \mathrm{original}\mathrm{volume} \\ \Rightarrow \mathrm{New}\mathrm{volume}=2\times \mathrm{original}\mathrm{volume} \end{gathered}$$

Hence, given statement is true.