The ratio between the curved surface area and the total surface area of a right circular cylinder is `1 : 2`. If the total surface area is `616 cm^(2)` then the volume of the cylinder is

Options

A. `1078 cm^(3)`
B. `1232 cm^(3)`
C. `1848 cm^(3)`
D. `924 cm^(3)`

Answer

A

Explanation

`(2pi RH)/(2pi RH + 2pi R^(2)) = (1)/(2) rArr (2pi R(H))/(2pi R(H + R)) = (1)/(2) rArr (H)/(H + R) = (1)/(2)`
`rArr H + R = 2H rArr H = R`
Now, `2pi R(H + R) = 616 rArr 4 pi R^(2) = 616 " " [ :' H = R]`
`:. 4 xx (22)/(7) xx R^(2) = 616 rArr R^(2) = (616 xx (7)/(88)) = 49 = 7^(2)`