Question

the ratio between the curved surface and total area surface of a cylinder is 1:2 . Find the volume of the cylinder ,given that it's total surface area is 616 cm^2

Answer 1

$\\ \frac{2\pi \: rh}{2\pi \: r( h+r )} = \frac{1}{2} \\ 2h = h+ r \\ h = r \\ 2\pi \: r(h + r) = 616 \\ 2\pi \: r(r + r) = 616 \\ 2 \times \frac{22}{7} \times 2 \times {r}^{2} = 616 \\ {r}^{2} = 616 \times 7 \div 88 \\ {r}^{2} = 49 \\ r = 7 \\ h = 7 \\ v = \pi {r}^{2} h = \frac{22}{7} \times 7 \times 7 \times 7 \\ v = 22 \times 49 \\ \: \: \: \: = 1078 {cm}^{3}$

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