Question
volume of the cone with radius of 10 and height of 15, use 3.14 for pie
Answers
GPT-4o mini
To find the volume of a cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, \( h \) is the height, and \( \pi \) (pi) is approximately \( 3.14 \).
For a cone with a radius \( r = 10 \) and a height \( h = 15 \):
1. Calculate \( r^2 \):
\[
r^2 = 10^2 = 100
\]
2. Plug \( r^2 \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (100)(15)
\]
3. Using \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times 100 \times 15
\]
4. Calculate \( 100 \times 15 \):
\[
100 \times 15 = 1500
\]
5. Now substitute back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1500
\]
6. Multiply \( 3.14 \) by \( 1500 \):
\[
3.14 \times 1500 = 4710
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{4710}{3} = 1570
\]
Therefore, the volume of the cone is approximately \( 1570 \) cubic units.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius, \( h \) is the height, and \( \pi \) (pi) is approximately \( 3.14 \).
For a cone with a radius \( r = 10 \) and a height \( h = 15 \):
1. Calculate \( r^2 \):
\[
r^2 = 10^2 = 100
\]
2. Plug \( r^2 \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (100)(15)
\]
3. Using \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times 100 \times 15
\]
4. Calculate \( 100 \times 15 \):
\[
100 \times 15 = 1500
\]
5. Now substitute back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1500
\]
6. Multiply \( 3.14 \) by \( 1500 \):
\[
3.14 \times 1500 = 4710
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{4710}{3} = 1570
\]
Therefore, the volume of the cone is approximately \( 1570 \) cubic units.