Question

A grain silo is built from two right circular cones and a right circular cylinder with internal measurements represented by the figure above. Of the following, which is closest to the volume of the grain silo, in cubic feet?

• A. $261.8$
• B. $785.4$
• C. $916.3$
• D. $1,047.2$

Answer 1

The correct option is D $1,047.2$

The volume of the grain silo can be found by adding the volumes of all the solids of which it is composed.

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:

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

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

$=1047.2$ cubic feet.(approx)