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 radius =2x and height =3x. Then,
`pir^2h=1617rArr 22/7xx(2x)^2xx3x=1617`
`x^3=(1617xx7/22xx1/2)=(7/2xx7/2xx7/2)=(7/2)^3`
`rArr x=7/2 cm`.
`:. R =7" cm and " h=21/2 cm`.
Total surface area `=2pir(h+r)`
`=2xx22/7x7xx(21/2+7)cm^2=770 cm^2`.