Question

5. The ratio between the curved surface area and the
total surface area of a right circular cylinder is
1:2. Find the volume of the cylinder if its total
surface area is 616 cm2.​

Answer 1

Answer:

Given that:Curved surface area : Total surface area =1:2

Curved surface area :616=1:2

Curved surface area=2616=308

⇒2πr(h+r)2πrh=21

⇒h+rh=21

⇒2h=h+r

⇒h=r

Curved Surface area=2πrh=2πr2=308 since h=r

⇒2×722r2=308

⇒r2=44308×7=49

⇒r=7cm

Since r=h

h=7cm

Volume of the cylinder=πr2h=722×7×7×7=1078cm3

∴ 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