CCGPS AG 3.5.3 Example 3

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 feet to the top of the dome and the radius of the dome is feet. How much grain can fit in the silo? Round to the nearest cubic foot.
  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.
  2. Calculate the volume of the cylinder using the formula . Substitute for and for .
  3. Calculate the volume of the hemisphere, which is half the volume of a sphere.
  4. Add the volume of the cylinder to the volume of the hemisphere to find the total volume of the grain silo.
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