Question

the ratio between the curved surface area and total surface of a right circular cyclinder is 1:2.Find the volume of the cylinder if its total surface area is 616 cm sq.

Answer 1

Given that, Curved surface area : Total surface area = 1:2 Curved surface area : 616 = 1:2 Curved surface area = 616 / 2 = 308 2πrh / 2πr(h+r) = 1/2h / (h+r) = 1/2 h+r = 2h ⇒ h = r Curved surface area = 2πrh = 2πr2 = 308 [Since h = r] 2 x 22/7 x r2 = 308 r2 = 308 x 7/44 r2 = 49 r = 7 cm ⇒ h = 7 cm Volume of the cylinder = πr2h  = 22/7 x 7 x 7 x 7 = 1078 cm3Volume of the cylinder is 1078 cu cm.

Answer 2

We have curved surface area= 2π*r*h

we have the circular surface  area= 2πr²

ATQ        2πr(h+r)= 616      ---(1)

        and  2*2πrh= 2πrh+ 2πr²

                            ⇒      h=r

Substituting value of h in (1)

                 we have 4πr²=616

                              ⇒   r²=59

                              ⇒   r=7

Volume of the cylinder is

                             ⇒  πr².h= πr³

                           

                             ⇒ = πr³=1078cm³