Question

The total surface area of a circular cylinder is $1540$sq.cm.If the height is four times the radius of the base , find the height of the cylinder.

Answer 1

Height$=4\times$ radius of the base.

$\Rightarrow h=4r$ where $r$ is the radius of the base

Total surface area$=1540$sq.cm

$2\pi r(r+h)=1540$

$\Rightarrow 2\pi r(r+4r)=1540$

$\Rightarrow 2\times \frac{22}{7}\times 5r^2=1540$

$\Rightarrow r^2=\frac{1540\times 7}{22\times 10}=49$

$\therefore r=7$

Hence height $=h=4r=4\times 7=28$cm