Question

A solid cylinder has total surface area of 462sq cm . Its curved surface area is one third of its total surface area . Find the volume of the cylinder?​

Answer 1

Given:-

• Total surface of cylinder = 462{cm}^{2}

• curved surface area is one-third of total surface

area

To find:-

Volume of cylinder = ?

Solution:-

Let r be the radius of the base and h be the height of the cylinder. Then,

Total surface area= 2\pi r(h+r)

Curved surface area = 2\pi\times r h

We have,

$\dashrightarrow\: \sf\ Curved surface area = \frac{1}{3}(total surface area)</p><p>[tex]\sf\ 2\pi rh= 154cm^2$ -------(1)

$\dashrightarrow\: \sf\ Total surface area = 462$

$\dashrightarrow\: \sf\ 2\pi rh + \frac{2}{\pi}r^2 = 462$

$\dashrightarrow\: \sf\ 154 + \frac{2}{\pi}r^2 = 462$

$\dashrightarrow\: \sf\ 2\times \frac{22}{7}=462-154$

$\dashrightarrow\: \sf\ r^2= 49 => r = 7cm$

From (1) , we have

$\dashrightarrow\: \sf\ 2\:times \frac{22}{7}\ \:times7\:time = 154$

$\dashrightarrow\: \sf\ h = \frac{7}{2}$

$\dashrightarrow\: \sf\ Volume of cylinder=\pi^2h=> \frac{22}{7} \times{7}{2}\times \frac{7}{2}= 539{cm}{3}$

$\dashrightarrow\: \underline{\boxed{\bf{\purple{volume= 539cm^3}}}}$

Answer 2

$\huge\underline\bold\red{AnswEr}$

Total surface area of a solid cylinder = 462 sq cm.

Curved surface area = 462/3 = 154 sq cm.

The area of the two ends = 462–154 = 308 sq cm.

The area of each end = 308/2 = 154 sq cm.

Radius of the cylinder = [154*7/22]^0.5 = 49^0.5 = 7 cm.

Height of the cylinder = 2pi*rh = 2*(22/7)*7*h = 154 or h = 154/44 = 3.5 cm.

Volume of cylinder = (22/7)*7^2*3.5 = 539 cm.