Question:
The circumference of the base of a cylinder is 88 cm and its height is 15 cm. Find its curved surface area and total surface area.
Solution:
Given :
Height, $h=15 \mathrm{~cm}$
Circumference of the base of the cylinder $=88 \mathrm{~cm}^{2}$
Let $r$ be the radius of the cylinder.
The circumference of the base of the cylinder $=2 \pi r$
$88=2 \times \frac{22}{7} \times \mathrm{r}$
$\mathrm{r}=\frac{88 \times 7}{2 \times 22}=14 \mathrm{~cm}$
Curved surface area $=2 \times \pi \times \mathrm{r} \times \mathrm{h}$
$=2 \times \frac{22}{7} \times 14 \times 15$
$=1320 \mathrm{~cm}^{2}$
Total surface area $=2 \times \pi \times \mathrm{r} \times(\mathrm{r}+\mathrm{h})$
$=2 \times \frac{22}{7} \times 14 \times(14+15)$
$=2552 \mathrm{~cm}^{2}$