Question

The ratio of total surface area and curved surface area are in the ratio of 2:3 . If the total surface area is 616 CM square. Find the radius and height of the cylinder. ​

Answer 1

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