Question

Find the volume of a cone with slant height of
29
29 feet and a radius of
20
20 feet. Use 3.14 for π. (The cone is not drawn to scale.) Click Here for Help Video 2



Click Here for Help Video




29
29 feet


20
20 feet


The height of the cone is
feet.



The volume of the cone is
cubic feet.

Answer 1

To find the volume of a cone, we can use the formula:

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

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

### Step 1: Find the height of the cone.

We are given the slant height (\( l \)) and the radius (\( r \)). We can use the Pythagorean theorem to find the height (\( h \)) of the cone. The relationship between the radius, height, and slant height can be defined as:

\[
l^2 = r^2 + h^2
\]

Given:
- Slant height \( l = 29 \) feet
- Radius \( r = 20 \) feet

We can rearrange the equation to solve for \( h \):

\[
h^2 = l^2 - r^2
\]

Now, plug in the values:

\[
h^2 = 29^2 - 20^2
\]

Calculating \( 29^2 \) and \( 20^2 \):

\[
29^2 = 841
\]
\[
20^2 = 400
\]

So,

\[
h^2 = 841 - 400 = 441
\]

Now, take the square root to find \( h \):

\[
h = \sqrt{441} = 21 \text{ feet}
\]

### Step 2: Calculate the volume of the cone.

Now that we have the height, we can substitute the radius and height into the volume formula:

\[
V = \frac{1}{3} \pi r^2 h
\]
\[
V = \frac{1}{3} \times 3.14 \times 20^2 \times 21
\]

Calculating \( 20^2 \):

\[
20^2 = 400
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 400 \times 21
\]
\[
V = \frac{1}{3} \times 3.14 \times 8400
\]

Calculate \( 3.14 \times 8400 \):

\[
3.14 \times 8400 = 26376
\]

Now divide by 3:

\[
V = \frac{26376}{3} = 8792
\]

### Final Answer

The volume of the cone is approximately **8792 cubic feet**.