Question
what is the approximate volume of a cone with a radius of 5 and height of 6
Answers
GPT-4o mini
The volume \( V \) of a cone can be calculated using 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:
- Radius \( r = 5 \)
- Height \( h = 6 \)
Substituting the values into the formula:
\[
V = \frac{1}{3} \pi (5^2)(6)
\]
Calculating the squared radius:
\[
5^2 = 25
\]
Now, substituting back into the formula:
\[
V = \frac{1}{3} \pi (25)(6) = \frac{1}{3} \pi (150) = 50\pi
\]
To get a numerical approximation, use \( \pi \approx 3.14 \):
\[
V \approx 50 \times 3.14 \approx 157
\]
So, the approximate volume of the cone is \( \approx 157 \) cubic units.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius of the base of the cone and \( h \) is the height.
Given:
- Radius \( r = 5 \)
- Height \( h = 6 \)
Substituting the values into the formula:
\[
V = \frac{1}{3} \pi (5^2)(6)
\]
Calculating the squared radius:
\[
5^2 = 25
\]
Now, substituting back into the formula:
\[
V = \frac{1}{3} \pi (25)(6) = \frac{1}{3} \pi (150) = 50\pi
\]
To get a numerical approximation, use \( \pi \approx 3.14 \):
\[
V \approx 50 \times 3.14 \approx 157
\]
So, the approximate volume of the cone is \( \approx 157 \) cubic units.