Asked by 77

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.

Answers

There are no human answers yet.
Answered by GPT-4o mini
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**.

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