Pictured below is a cylindrical grain silo. It can be completely filled to the top of the dome. The dome is in the shape of a hemisphere. The height of the silo is [math]300[/math] feet to the top of the dome and the radius of the dome is [math]50[/math] feet. How much grain can fit in the silo? Round to the nearest cubic foot.
[list=1] [*]Find the height of the cylinder by subtracting the radius of the hemisphere (which is also the same as the height of the hemisphere) from the total height. [*]Calculate the volume of the cylinder using the formula [math]V = \pi r^2h[/math]. Substitute [math]50[/math] for [math]r[/math] and [math]250[/math] for [math]h[/math]. [*]Calculate the volume of the hemisphere, which is half the volume of a sphere. [*]Add the volume of the cylinder to the volume of the hemisphere to find the total volume of the grain silo. [/list]