A grain silo is made up of two right circular cones and a right circular cylinder, with the internal dimensions shown in the figure above. Which of the following comes closest to the grain silo's volume in cubic feet?

The volume of the grain silo can be calculated by adding the volumes of all the solids that make it up. The silo is made up of a cylinder with height 10 feet and base radius 5 feet and two cones, each having height 5 feet and base radius 5 feet.

The formulas volume of cylinder $\pi r^{2}h$ and volume of cone $\frac{1}{3}\pi r^{2}h$ can be used to determine the total volume of the silo.

Since the two cones have identical dimensions, the total volume, in cubic feet, of the silo is given by:

$V=\pi {\left(5\right)}^2\left(10\right)+\left(2\right)\left(\frac{1}{3}\right)\pi {\left(5\right)}^2\left(5\right)$

$=\left(\frac{4}{3}\right)\left(250\right)\pi$

$=1047.2\text{ cubic feet.(approx)}$