Question

Taylor uses a cone-shaped feeder, with a diameter of 18 inches and a height of 11 inches, to feed her chickens.
How many cubic in of feed can this feeder hold?
Use 3.14 for pi.
Enter your answer in the box as a decimal rounded to the nearest tenth.
in³
PLEASE HELP.

Answer 1

Answer: 932.6 in³

Step-by-step explanation:

Hi again! We will need to use the volume formula of a cone to solve this one because we are asked to find how much food could fit in the whole feeder. Make sure to not get confused between radius and diameter when solving.

Volume of Cone formula: $\[\fbox{ \( V = \frac{1}{3} \pi r^2 h \)}\]$

• $\item \( V \) is the volume of the cone$
• $\item \( \pi \) is a constant (approximately 3.14)$
• $\item \( r \) is the radius of the base of the cone(half diameter)$
• $\item \( h \) is the height of the cone\end{itemize}$

Again, we are given diameter so we will need to convert that to radius.

Solving:

Given : $d=2r$ → $18=2r$ → $\fbox{r=9}$, $h=11$

Now lets plug into the Volume equation and solve:

$\begin{itemize} \item \(V = \frac{1}{3} \pi r^2 h\)}\) \item \({\(V = \frac{1}{3} \times 3.14 \times 9^2 \times 11\)}\) \item \({\(V = \frac{1}{3} \times 3.14 \times 81 \times 11\)}\) \item \({\(V = \frac{1}{3} \times 3.14 \times 891\)}\) \item \(\fbox{\(V \approx 932.6 \, \text{in}^3\)}\)\end{itemize}$

I used 3.14 for $\pi$ since the problem asked, and I rounded to the nearest tenth as the problem asked.

That's it!