Question

A solid cylinder has total surface area of 1386 $c{m}^2$. Its curved surface area one-ninth of its total surface area. Find the radius and height of the cylinder.

Answer 1

Total surface area $=2\pi r^{2}h+2\pi r^2=1386c{m}^2$

$\Rightarrow CSA=\frac{1}{9}.TSA$

$\Rightarrow 2\pi rh=\frac{1}{9}(2\pi rh+2\pi r^2)$

$\Rightarrow 18\pi rh=2\pi rh+2\pi r^2$

$\Rightarrow 16\pi rh=2\pi r^2$

$r=8h$

Also,

$\Rightarrow 2\pi rh=\frac{1}{9}\times 1386$

$\Rightarrow 2\pi \times 8h\times h=\frac{1}{9}\times 1386$

$\Rightarrow h^2=\frac{1386}{9\times 16\pi }=\frac{1386}{9\times 16}\frac{7}{22}=\frac{49}{16}$

$\Rightarrow h=\frac{7}{4}cm$

$\Rightarrow r=8h=8\times \frac{7}{4}=14cm$

$\therefore$ radius $=14cm$ length $=\frac{7}{4}cm.$

Hence, solved.