Question:
A solid cylinder has a total surface area of $462 \mathrm{~cm}^{2}$. |its curved surface area is one-third of its total surface area. Find the radius and height of the cylinder. (Take $\pi=3.14$ ).
Solution:
Given that
Curved or lateral surface area = 13 * total surface area
$2 \pi r h=1 / 3\left(2 \pi r h+2 \pi r^{2}\right)$
$4 \pi r h=2 \pi r^{2}$
2h = r
Total surface area $=462 \mathrm{~cm}^{2}$
Curved surface area = 1/3 ∗ 462
2πrh = 154
$2 * 3.14 * 2 * h^{2}=154$
$h^{2}=49 / 4$
h = 49/4 cm
= 7/2 cm
Now r = 2h
Therefore r = 2 * 7/2 cm = 7cm
The height and the radius of the cylinder is 7/2 cm and 7 cm respectively.