Question

The total surface area of a solid right circular cylinder is $231{cm}^2$. Its curved surface area is two thirds of the total surface area. Find height of the cylinder.

Answer 1

We know that the total surface area of a cylinder $=2\pi rh+2\pi r^2$

curved surface area $=2\pi rh$

According to the question,

$\frac{2}{3}\times (2\pi rh+2\pi r^2)=2\pi rh$

$2\pi r[\frac{2}{3}\times (h+r\left)\right]=2\pi rh$

$\frac{2}{3}\times (h+r)=h$

$2h+2r=3h$

$h=2r$

So,

$2\pi rh+2\pi r^2=231$

$2\pi r(h+r)=231$

$2\pi r\times 3r=231$

$r=3.5cm$

And $h=2r$

$h=7cm$

Hence, this is the answer.