Question

a solid cylinder has a total surface area of 231cm2 . its curved surface area is 2/3 of the total surface area . find the volume of the cylinder

Answer 1

let radius be=r
      & height=h
Area of the solid cyl=2πr²+2πrh=231
As per problem ⇒ 2πrh= 2(2πr²+2πrh)/3
                       ⇒  2πrh=4πr²
                       ⇒       h=2r
hence⇒6πr²=231
             πr²=231/6
               r=√12.254

volume⇒πr²h=2πr³=2π(√12.254)³=269.48cm³