Question

What is the volume of this cone?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

ratio 10 ft
height 15 ft

cubic feet

Answer 1

To find 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

From the problem, we have:
- The diameter of the cone is 10 ft, which means the radius \( r \) is half of that:

\[
r = \frac{10}{2} = 5 \text{ ft}
\]

- The height \( h \) of the cone is 15 ft.

Now, substitute the values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15
\]

First, calculate \( (5)^2 \):

\[
(5)^2 = 25
\]

Now substitute this value back into the equation:

\[
V = \frac{1}{3} \times 3.14 \times 25 \times 15
\]

Now perform the multiplication:

\[
25 \times 15 = 375
\]

Then, substitute this into the volume calculation:

\[
V = \frac{1}{3} \times 3.14 \times 375
\]

Now calculate \( 3.14 \times 375 \):

\[
3.14 \times 375 = 1177.5
\]

Now, divide by 3:

\[
V = \frac{1177.5}{3} \approx 392.5
\]

Finally, rounding to the nearest hundredth, the volume of the cone is:

\[
V \approx 392.50 \text{ cubic feet}
\]

So the volume of the cone is **392.50 cubic feet**.