Question

A solid cylinder has a total surface area of $231c{m}^2$. Its curved surface area. Find the volume of the cylinder?

• A. $270c{m}^3$
• B. $269.5c{m}^3$
• C. $256.5c{m}^3$
• D. $289.5c{m}^3$

Answer 1

Answer: (B)

$269.5c{m}^3$

let radius be=$r$ & height=$h$

Area of the solid cylinder =$2\pi r^2+2\pi rh$=231

As per problem

Curved surface are =$\frac{2}{3}$ Total Surface are

$⟹2\pi rh=\frac{2}{3}(2\pi r^2+2\pi rh)$

$⟹2\pi rh=4\pi r^2⟹h=2r$

Hence Total surface area$=6\pi r^2=231⟹\pi r^2=\frac{231}{6}⟹r=\sqrt{12.254}cm$

volume of cylinder=$\pi r^{2}h=2\pi r^3=2\pi (\sqrt{12.254}{)}^3=269.48c{m}^3$