Question

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

Answer 1

Total surface area (T.S.A) = 616 cm2 Let r be the radius of cylinder and h be the radius of cylinder.

As per given statement: (curved surface area / (total surface area) = 1212 or CSA = 1212TSA CSA = 1212 x 616 = 308 ⇒ CSA = 308 cm2

$Now,$

$TSA = 2πrh + 2πr2$

$⇒ 616 = CSA + 2πr2$

$⇒ 616 = 308 + 2πr2$

$⇒ 2πr2 = 616 – 308$

$⇒ 2πr2 = 308$

$⇒ r2 = 308/2π$

$⇒ r2 = 49 or r = 7 cm …(1) As, CSA = 308 cm2 2πrh = 308$

$⇒ 2 x 227227 x 7 x h = 308 (using (1))$

$⇒ h = 7 cm$

$Now,$

Volume of cylinder$= πr2h = 227227 x 7 x 7 x 7 = 1078$

Therefore ,1078cm^2 ANSWER

HOPE SO IT IS HELPFUL..✌️❣️..

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