Question:
Find the curved surface area and total surface area of a cylinder, the diameter of whose base is 7 cm and height is 60 cm.
Solution:
Let $r$ and $h$ be the radius and the height of the cylinder.
Given :
$\mathrm{r}=\frac{7}{2} \mathrm{~cm}$
$\mathrm{~h}=60 \mathrm{~cm}$
Curved surface area of the cylinder $=2 \pi \times \mathrm{r} \times \mathrm{h}$
$=2 \times \frac{22}{7} \times \frac{7}{2} \times 60$
$=22 \times 60=1320 \mathrm{~cm}^{2}$
Total surface area of the cylinder $=2 \pi \times \mathrm{r} \times(\mathrm{r}+\mathrm{h})$
$=2 \times \frac{22}{7} \times \frac{7}{2} \times\left(\frac{7}{2}+60\right)=22 \times \frac{127}{2}=11 \times 127=1397 \mathrm{~cm}^{2}$