The sum of the radius of the base and height of a solid cylinder is 37m. If the total surface area of the solid cylinder is `1628\ c m^2dot` Find the volume of the cylinder.

Explanation

Let `r` be the radius and `h` be the height.
Sum of radius and height of a cylinder`=37 m`
`r+h=37 m`
Total surface area of a solid cylinder`=1628 m^2`
Total surface area of the cylinder`=2pirh+2pir^2=2pir(h+r)`
According to the question:
`2pir(h+r)=1628`
`2times22/7r(37)=1628`
`r=1628times7/2times22times37=7 m`
`r+h=37`
`h=37-r`
`h=37-7=30 m`
Volume`=pir^2h`
`=(22/7times7times7times30) m^3`
`=4620 m^3`