Question

The ratio between the curved surface and total surface of a cylinder is 1:2. Find the
volume of the cylinder, given that its total surface area is 616 cm​

Answer 1

Step-by-step explanation:

2πrh/2πr(r+h)=1/2

h/r+h=1/2

cross multiply

2h=r+h

r=h

4πrh=616

r=7

volume = π7^3

=1078cm^3

Answer 2

Step-by-step explanation:

It's quite easy bro,

T.S.A of cylinder = 2πr(h+r) ....................(I)

C.S.A of cylinder = 2πrh.............(ii)

Diving eq. (I) by (ii), we get :-

2πrh/2πr(h+r) = 1/2 ( given)

=> h/h+r = 1/2

=> 2h = h+r

Therefore, r = 2h-h = h

Also, T.S.A of cylinder = 2πr(h+r)

=> 616cm2 = 2πr(h+r)

=> 2πh(h+h) = 616cm2 ( Since, r = h)

=> 2 × 22/7 × h × 2h = 616cm2

=> 44/7 × 2h^2 = 616 cm2

=> 88/7 × h^2 = 616 cm2

=> h^2 = 616 ÷ 88/7

=> h^2 = 616 × 7/88

=> h^2 = 7 × 7

=> h^2 = 49

Therefore, h = √49

= 7cm

And, r = h = 7cm

So, Volume of cylinder = πr^2h

= (22/7 × 7^2 × 7) cm^3

= (22 × 49) cm^3

= 1078 cm^3

Hope it helps :)