Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is $1:2$. Find the volume of the cylinder if its total surface area is $616$ cm sq.

Answer 1

Given that:Curved surface area $:$ Total surface area $=1:2$

Curved surface area $:616=1:2$

Curved surface area$=\frac{616}{2}=308$

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

$\Rightarrow \frac{h}{h+r}=\frac{1}{2}$

$\Rightarrow 2h=h+r$

$\Rightarrow h=r$

Curved Surface area$=2\pi rh=2\pi r^2=308$ since $h=r$

$\Rightarrow 2\times \frac{22}{7}{r}^2=308$

$\Rightarrow r^2=\frac{308\times 7}{44}=49$

$\Rightarrow r=7$cm

Since $r=h$

$h=7$cm

Volume of the cylinder$=\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 7=1078{cm}^3$

$\therefore$ Volume of the cylinder is $1078$ cu cm.