Question

The total surface area of a solid right circular cylinder is $1540{cm}^2$. If the height is four times the radius of the base , then find the height of the cylinder ?

Answer 1

Let the radius of the cylinder be $r$.
Given: height is $4r$
Total surface area of cylinder: $2\pi rh+2\pi r^2=2\pi r\left(4r\right)+2\pi r^2=8\pi r^2+2\pi r^2=10\pi r^2$
Given: $10\pi r^2$=1540
$⟹r^2=\frac{154}{\pi }$
Using $\pi \approx \frac{22}{7}$
$r^2=\frac{154}{22/7}=\frac{154\times 7}{22}=49$
$⟹r=7cm$
Therefore, height = $4\times 7cm=28cm$