Question

at the local animal shelter there is a cone shaped dog food dispenser if thedispenser is 54 cenitermeters tall and has a diameter of 24 centimeters at the top what is the volume to the nearest cuboc centimeter

Answer 1

To calculate the volume of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \(V\) is the volume,
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.

Given:
- Height \(h = 54\) cm
- Diameter = 24 cm, so the radius \(r = \frac{24}{2} = 12\) cm.

Now, substitute the values into the formula:

\[
V = \frac{1}{3} \pi (12)^2 (54)
\]

Calculating \(12^2\):

\[
12^2 = 144
\]

Now substituting this back into the volume formula:

\[
V = \frac{1}{3} \pi (144) (54)
\]

Calculating \(144 \times 54\):

\[
144 \times 54 = 7776
\]

So now we have:

\[
V = \frac{1}{3} \pi (7776)
\]

Now calculate \(\frac{1}{3} \times 7776\):

\[
\frac{7776}{3} = 2592
\]

Thus,

\[
V = 2592 \pi
\]

Using the value of \(\pi \approx 3.14\):

\[
V \approx 2592 \times 3.14 \approx 8145.28
\]

Rounding to the nearest cubic centimeter, the volume is approximately:

\[
\boxed{8145} \text{ cubic centimeters}
\]