Question

the ratio between the curved surface area and the total surface of a cylinder is 1 : 2 find the volume of the cylinder given that its total surface area is 616 CM square

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) = 1/2
h / (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 cm3

Volume 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