Question

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 cm.​

Answer 1

Answer:

Volume of cylinder is 22,617.42cm³.

Explanation:

Given ratio of surface area :total surface area of cylinder =1:2.

As surface area of cylinder is 2׶×r×h.

And total surface area is ¶×r×(r + h).

=>$\frac{2\pi rh}{\pi r(r + h)} \frac{1}{2}$

=>$\frac{2h}{(r + h)} = \frac{1}{2}$

=>$4h = (r + h)$

=>$3h = r$

Given total surface area =616cm²

Therefore,

=>$\pi \times r(r + h) = 616 \\=>\pi{r}^{2} + \pi rh = 616 \\=>\pi {(3h)}^{2} + \pi(3h)h = 616 \\ =>9 {h}^{2} \pi + 3 {h}^{2} \pi = 616 \\ =>12 {h}^{2} \pi = 616 \\=> \pi {h}^{2} = \frac{616}{12}$

$\pi \: { (\frac{r}{3} )}^{2} = \frac{616}{12}$

$\pi {r}^{2} = \frac{616 \times 9}{12}$

$\pi {r}^{2} = 462$

$r = \sqrt{147} cm$

$volume = \pi {r}^{3} h$

$volume = \pi \times 147 \sqrt{147} \times ( \frac{r}{3} )$

$volume = \pi \times 147 \sqrt{147} \times \frac{ \sqrt{147} }{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi {147}^{2} }{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 22617.42 \: {cm}^{3}$

Answer 2

We have curved surface area= 2π*r*h

we have the circular surface  area= 2πr²

ATQ        2πr(h+r)= 616      ---(1)

        and  2*2πrh= 2πrh+ 2πr²

                            ⇒      h=r

Substituting value of h in (1)

                 we have 4πr²=616

                              ⇒   r²=59

                              ⇒   r=7

Volume of the cylinder is

                             ⇒  πr².h= πr³

                           

                             ⇒ = πr³=1078cm³