Question

A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number.

Answer 1

Area of a cylinder is the area of the top + the area of the bottom + the area of the wrap-around (lateral)
top: pi*r*r=81pi
bottom: 81pi
lateral: 2pi*r*h=18pi*h, h is unknown, but you don't have to solve it. 

add them up: 81pi +81pi + 18h*pi=1850 
pi*h=(1850-162pi)/18, (plug this in the volume formula below.)

volume of a cylinder: the area of the base × the height =81pi*h
volume=81[1850-162pi)/18]
use your calculator: V=6036

please double check my calculation by yourself.