The ratio between the radius of the base and the height of the cylinder is 2:3. If its volume is 1617 `cm^3` , the total surface area of the cylinderical is

Options

A. `308 cm^(2)`
B. `462 cm^(2)`
C. `540 cm^(2)`
D. `770 cm^(2)`

Answer

D

Explanation

Let the radius be 2x cm and the height be 3x cm.
Then, volume `= pi xx (2x)^(2) xx 3x = (22)/(7) xx 12 xx x^(3)`
`:. (22)/(7) xx 12 xx x^(3) = 1617 rArr x^(3) = (1617 xx (1)/(12) xx (7)/(22)) = (49 xx 7)/(8) = ((7)/(2))^(3)`
`rArr x = (7)/(2) rArr r = 7 cm and h = (21)/(2) cm`
`:.` total surface area `= 2pi rh + 2pi r^(2) = 2pi r (h + r)`
`= {2 xx (22)/(7) xx 7 xx ((21)/(2) + 7)} cm^(2) = 770 cm^(2)`