Question

the ratio between the curved surface and total surface of a cylinder is 1:2 find the volume of the the cylinder , given that it's total surface area is 616cm square

Answer 1

Let the Curved surface are and the total surface are be x and 2x respectively.

Given, 2x = 616
             x = 308 =  Curved Surface Area = 2 x (22/7) x r x h

Solving it we get that r x h = 49

Now 2 x (22/7) x r x (r + h) = 616

22/7 x r x (r + h) = 308

2 x r x (r + h) = 196

r^2 + (r x h) = 98
 
As (r x h) = 49,

r^2 + 49 = 98

r^2 = 49

r = 7cm

r x h = 49

7 x h = 49

h= 7

Volume = (22/7) x r x r x h =(22/7) x 7 x 7 x 7 =154 x 7 =700 + 350 + 28 =1078 cm^3