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.
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**.
\[
V = \frac{1}{3} \pi r^2 h
\]
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**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.