The radius of a cylinder is 5m more than its height. If the curved surface area of the cylinder is 792m2, what is the volume of the cylinder? (in m3) (a) 5712 (b) 5244 (c) 5544 (d) 5306 (e) 5462

Options

A. 5712
B. 5244
C. 5544
D. 5306

Answer

C

Explanation

Let height be xm
them,Radius =(x + 5)m
Curved surface area of cylinder `=2pirh`
`792=2xx22/7xx(x+5)xx xrArr(396xx7)/22=x^2+5x`
`126=x^2+5x`
`x^2+5x-126=0`
`x^2+14x-9x=126=0`
`x(x+14)-9(x-14)=0`
`(x-9)(x-14)=0`
`x=9,x=-14m`
we have to take height, x=9m because height can't be negative.
So, leaving the value of x = -14
`:." Height "=9m"and radius "=9+5=14m`
Hence, volume
`=pi^2rh=22/7xx14xx14xx9=44xx126=5544m^3`