Question
volume of the cone with radius of 7and height of 12
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,
- \( h \) is the height.
For a cone with a radius \( r = 7 \) and a height \( h = 12 \):
\[
V = \frac{1}{3} \pi (7)^2 (12)
\]
Calculating it step by step:
1. Calculate \( r^2 \):
\[
7^2 = 49
\]
2. Multiply by the height \( h \):
\[
49 \times 12 = 588
\]
3. Now, multiply by \( \pi \) and then divide by 3:
\[
V = \frac{1}{3} \pi (588) = \frac{588\pi}{3} = 196\pi
\]
So, the volume of the cone is approximately:
\[
V \approx 196 \times 3.14159 \approx 615.75
\]
Thus, the volume of the cone is \( 196\pi \) cubic units or approximately \( 615.75 \) cubic units.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( r \) is the radius,
- \( h \) is the height.
For a cone with a radius \( r = 7 \) and a height \( h = 12 \):
\[
V = \frac{1}{3} \pi (7)^2 (12)
\]
Calculating it step by step:
1. Calculate \( r^2 \):
\[
7^2 = 49
\]
2. Multiply by the height \( h \):
\[
49 \times 12 = 588
\]
3. Now, multiply by \( \pi \) and then divide by 3:
\[
V = \frac{1}{3} \pi (588) = \frac{588\pi}{3} = 196\pi
\]
So, the volume of the cone is approximately:
\[
V \approx 196 \times 3.14159 \approx 615.75
\]
Thus, the volume of the cone is \( 196\pi \) cubic units or approximately \( 615.75 \) cubic units.