A solid cylinder has a total surface area of 462 cm2.

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.