Question

If the volume of a cylinder of height 7 cm is 448 pie cm cube, find its lateral surface area and total surface area

Answer 1

Dear Student,
We are given height h of the cylinder is 7cm
and its volume V is 448$\mathrm{\pi }{\mathrm{cm}}^3$. Let r be the radius of the cylinder.
Now, we know volume of a cylinder is
$$\begin{gathered} V={\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow 448\mathrm{\pi }={\mathrm{\pi r}}^2\left(7\right) \\ \Rightarrow {\mathrm{r}}^2=\frac{448}{7}=64 \\ \Rightarrow \mathrm{r}=\pm 8 \\ \Rightarrow \mathrm{r}=8\mathrm{cm}(\mathrm{since}\mathrm{radius}\mathrm{can}\text{'}\mathrm{t}\mathrm{be}\mathrm{negative}) \end{gathered}$$
Now, Lateral surface area of a cylinder = $2\mathrm{\pi rh}$
=2$\mathrm{\pi }$(8)(7)
=112$\mathrm{\pi }$ cm²
And Total surface area of a cylinder = ​$2\mathrm{\pi rh}$ + 2$\mathrm{\pi }$r²
=$2\mathrm{\pi r}(\mathrm{h}+\mathrm{r})$
=2$\mathrm{\pi }$(8)(7+8)
=240$\mathrm{\pi }$ cm²
Regards