A solid cylinder has surface area of 231cm2 Its curved surface area is 2/3 of the total surface area - Maths - Surface Areas and Volumes

Question

A solid cylinder has surface area of 231cm2 Its curved surface
area is 2/3 of the total surface area Find the volume of
cylinder

Manish Bharti · Accepted Answer

We are given,
Total surface area of cylinder = 231 $c m^{2}$
$\Rightarrow 2 π r h + 2 π r^{2} = 231$ ------ (1)
Curved surface area $= 2 / 3 \times 231 = 154 c m^{2}$
$\Rightarrow 2 π r h = 154$ ------ (2)
Substituting $2 π r h = 154$ in equation (1), we get
$154 + 2 π r^{2} = 231 2 π r^{2} = 77 r^{2} = \frac{77}{2} \times \frac{7}{22} \Rightarrow r = \frac{7}{2}$
Substituting the value of r in equation (2), we get
$2 π \times \frac{7}{2} \times h = 154 h = \frac{154}{22} \Rightarrow h = 7$
Volume of cylinder is
$= π r^{2} h = \frac{22}{7} \times \frac{7^{2}}{2^{2}} \times 7 = 269.5 c m^{3}$

A solid cylinder has surface area of 231cm2 Its curved surface area is 2/3 of the total surface area . Find the volume of cylinder