Question

the ratio between curved surface and total surface is 1 : 2
find the volume of cylinder if total surface area is 616 cm2​

Answer 1

Answer:

volume of cylinder is 1078 cm³

Step-by-step explanation:

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

=> 2h= h+r

=> h=r

=> curved surface area=2πrh=2πr²=308

since h=r

=> 2×22/7 r²=308

=> r² = 308×7/44= 49

=> r² = 49

=> r= 7cm.

since r= h

h= 7cm.

volume of cylinder= πr²h = 22/7× 7²×7

=> 1078cm³

therefore volume of the cylinder is 1078 cu. cm.

Answer 2

Answer:

given csa:tsa =1:2

therefore tsa = 2×csa

tsa = 616 cm²

TSA = 2πr (h + r)

CSA = 2πrh

csa:tsa = 1:2

2πrh : 2πr(h+r) = 1:2

(2πrh)/(2πr(h+r) = 1/2

    (h) /(h+r)       = 1/2    [on cancelling 2πr on both num. and den.]

         2h        =  h+r

           2h-h     = r

              h      = r

so height and the radius are equal

tsa = 616cm²

2πr(h+r)=616cm²

2πr(r+r)  = 616   [as h=r]

2πr(2r)    =  616

4πr²       =  616

   πr²   = 616/4

       r² = 154/π

        r² = 49

        r  = 7

hence r=h=7cm

volume of cylinder = πr²h

                               = π7²×7 =  π7³

                               =  22/7  × 7³

                                = 22×7²

                                =1078cm³