Question

The rato 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 $616c{m}^2$.

Answer 1

Given that,
Curved surface area : Total surface area = 1:2
Curved surface area : 616 = 1:2

Curved surface area = 616 / 2 = 308
$2\pi rh÷2\pi r(h+r)=1/2$
h / (h+r) = 1/2
h+r = 2h
⇒ h = r

Curved surface area =$2\pi rh=2\pi r^2=308$[Since h = r]

2 x 22/7 x $r^2$ = 308
$r^2=308\times 7/44$
$r^2=49$
r = 7 cm

⇒ h = 7 cm

Volume of the cylinder = $\pi r^{2}h$
= 22/7 x 7 x 7 x 7
= $1078c{m}^3$

Volume of the cylinder is $1078c{m}^3$