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][br][*]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.[br][*]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].[br][*]Calculate the volume of the hemisphere, which is half the volume of a sphere.[br][*]Add the volume of the cylinder to the volume of the hemisphere to find the total volume of the grain silo.[br][/list][br][br]This applet is provided by Walch Education as supplemental material for the [i]CCGPS Analytic Geometry[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.