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,
- \( \pi \) is approximately 3.14.
Given:
- The diameter of the cone is 20 cm, so the radius \( r \) is half of that:
\[ r = \frac{20}{2} = 10 , \text{cm} \] - The height \( h \) is 15 cm.
Now we can plug these values into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (10)^2 \times 15 \]
Calculating \( (10)^2 \):
\[ (10)^2 = 100 \]
Now substituting this value back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 100 \times 15 \]
Calculating \( 100 \times 15 \):
\[ 100 \times 15 = 1500 \]
Now substituting again:
\[ V = \frac{1}{3} \times 3.14 \times 1500 \]
Calculating \( 3.14 \times 1500 \):
\[ 3.14 \times 1500 = 4710 \]
Finally, calculating:
\[ V = \frac{4710}{3} = 1570 \]
So, the volume of the cone is:
\[ \boxed{1,570} , \text{cubic centimeters} \]