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Question
Find the height and volume of a cone with slant height of 41 feet and a radius of 40 feet. Use 3.14 for pi. Click Here for Help Video 2. Click HERE for help video. Click HERE for Formulas Sheet.

Answer 1

To find the height and volume of a cone with a given slant height and radius, we can use the following formulas:

1. **Height (h)** can be found using the Pythagorean theorem:
\[
s^2 = r^2 + h^2
\]
where \( s \) is the slant height, \( r \) is the radius, and \( h \) is the height.

2. **Volume (V)** of the cone is given by the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]

Given:
- Slant height (\( s \)) = 41 feet
- Radius (\( r \)) = 40 feet
- Use \( \pi = 3.14 \)

### Step 1: Find the height

Using the Pythagorean theorem:
\[
41^2 = 40^2 + h^2
\]
Calculating \( 41^2 \) and \( 40^2 \):
\[
1681 = 1600 + h^2
\]

Now, solving for \( h^2 \):
\[
h^2 = 1681 - 1600
\]
\[
h^2 = 81
\]

Now, take the square root to find \( h \):
\[
h = \sqrt{81} = 9 \text{ feet}
\]

### Step 2: Find the volume

Now that we have the height, we can calculate the volume:
\[
V = \frac{1}{3} \pi r^2 h
\]
Substituting the values:
\[
V = \frac{1}{3} \cdot 3.14 \cdot (40)^2 \cdot 9
\]
Calculating \( (40)^2 \):
\[
(40)^2 = 1600
\]
Now substitute this back:
\[
V = \frac{1}{3} \cdot 3.14 \cdot 1600 \cdot 9
\]

Calculating \( 1600 \cdot 9 \):
\[
1600 \cdot 9 = 14400
\]
Now substitute back into the volume equation:
\[
V = \frac{1}{3} \cdot 3.14 \cdot 14400
\]

Now, calculate \( 3.14 \cdot 14400 \):
\[
3.14 \cdot 14400 = 45144
\]
Finally,
\[
V = \frac{1}{3} \cdot 45144 \approx 15048
\]

### Final Answers:
- Height \( h = 9 \) feet
- Volume \( V \approx 15048 \) cubic feet