Question

The T.S.A. of right circular cylinder is $3432$ ${cm}^2$ . Its C.S.A. is $\frac{5}{26}$ of its T.S.A. Determine the radius of the base and height.

Answer 1

Total Surface area of the cylinder$=3432sq.cm$

Given:$\frac{5}{26}\times$ Total Surface area of the cylinder$=$curved Surface area of the cylinder

$\Rightarrow \frac{5}{26}\times 2\pi r(r+h)=2\pi rh$

$\Rightarrow 5r+5h=26h$

$\Rightarrow 5r=26h-5h$

$\Rightarrow 5r=21h$

$\Rightarrow h=\frac{5}{21}r$

Total Surface area of the cylinder$=2\pi r(r+h)=3432sq.cm$

$\Rightarrow \pi r(r+\frac{5}{21}r)=1716sq.cm$

$\Rightarrow \pi r\left(\frac{21r+5r}{21}\right)=1716sq.cm$

$\Rightarrow \pi r\left(\frac{26r}{21}\right)=1716sq.cm$

$\Rightarrow r^2=\frac{1716\times 21}{\frac{22}{7}\times 26}=441$

$\Rightarrow r=21cm$

We have $h=\frac{5}{21}r=\frac{5}{21}\times 21=5cm$

$\therefore h=5cm$ and $r=21cm$