Question

The ratio between curved surface area and total surface area of a right circular cylinder is 2 : 3. Find ratio between height and radius of cylinder.

Answer 1

$\frac{2 \pi rh}{2 \pi r(r+h)}= \frac{2}{3} \\ \frac{h}{r+h}= \frac{2}{3} \\ 3h=2r+2h \\ 3h-2h=2r \\ h=2r \\ \frac{h}{r}= \frac{2}{1}$
Ratio of height to radius = 2:1

Answer 2

CSA = 2πrh
TSA = 2πr(r+h)

Given that CSA:TSA = 2:3

$\frac{2 \pi rh}{2 \pi r(r+h)} = \frac{2}{3} \\ \\ \frac{h}{r+h} = \frac{2}{3} \\ \\ 3h=2(r+h)=2r+2h \\ \\ 3h-2h=2r \\ \\ h=2r \\ \\ \frac{h}{r}=2 \\ \\ h:r=2:1$