Question

The volume of a solid cylinder is ${\text{448π cm}}^3$ and height $7\text{cm}$. Find its lateral surface area and total surface area ?

Answer 1

Volume of solid cylinder $=448\mathrm{\pi }{\mathrm{cm}}^3$

And height of the cylinder$=\text{base area×height}$ $=7\text{cm}$

We know that volume of the cylinder $=\mathrm{\pi }{\text{r}}^2\text{h}$

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

So $\mathrm{\pi }{\text{r}}^2\text{h=448π}$

$$\begin{gathered} \sout{\mathrm{\pi }}{\text{r}}^2\text{h=448}\sout{\mathrm{\pi }} \\ {\text{r}}^2\text{×7=448} \\ {\mathrm{r}}^2=\frac{448}{7}=64 \\ \mathrm{r}=\sqrt{64}=8\mathrm{cm} \end{gathered}$$

Lateral surface area $=2\mathrm{\pi }\text{rh}$

After putting the values of $\text{r}$ and $\text{h}$

$2\mathrm{\pi rh}=2\times \frac{22}{7}\times 8\times 7=352{\text{cm}}^2$

Total surface area${\text{=2πrh+2πr}}^2$ $=2\mathrm{\pi r}(\mathrm{r}+\mathrm{h})=2\times \frac{22}{7}\times 8(8+7)=2\times \frac{22}{7}\times 8\left(15\right)=2\times \frac{22}{7}\times 120=\frac{5280}{7}=754.28{\text{cm}}^2$