Question

the ratio between the curved surface area and total surface area surface area of a right circular cylinder is 1 is to 2 if the total surface area is 616 CM square find the volume of the cylinder

Answer 1

Answer:let  radius =r cm and height=h cm

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= π7³=1078cm³

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Answer 2

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) = 1/2h+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.