Question

What is the volume of this cone?
Height=19 Diameter= 22
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

where \( r \) is the radius of the base of the cone and \( h \) is the height.

Given:
- Height \( h = 19 \)
- Diameter \( = 22 \), so the radius \( r \) is:

\[
r = \frac{\text{Diameter}}{2} = \frac{22}{2} = 11
\]

Now, substitute the values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19
\]

First, calculate \( 11^2 \):

\[
11^2 = 121
\]

Now substitute that back into the formula:

\[
V = \frac{1}{3} \times 3.14 \times 121 \times 19
\]

Next, calculate \( 121 \times 19 \):

\[
121 \times 19 = 2299
\]

Now substitute that value back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 2299
\]

Now calculate \( 3.14 \times 2299 \):

\[
3.14 \times 2299 \approx 7210.86
\]

Finally, divide by 3:

\[
V \approx \frac{7210.86}{3} \approx 2403.62
\]

So the volume of the cone, rounded to the nearest hundredth, is:

\[
\boxed{2403.62}
\]