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 of the base, and
- \( h \) is the height of the cone.
Given that the diameter of the cone is 20 cm, the radius \( r \) can be calculated as follows:
\[ r = \frac{diameter}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]
The height \( h \) is given as 15 cm. Now, substituting \( r \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times (10 , \text{cm})^2 \times 15 , \text{cm \]
Calculating \( (10 , \text{cm})^2 \):
\[ (10 , \text{cm})^2 = 100 , \text{cm}^2 \]
Now substituting this back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 100 , \text{cm}^2 \times 15 , \text{cm} \]
Calculating the volume step by step:
- Multiply \( 100 , \text{cm}^2 \) by \( 15 , \text{cm} \):
\[ 100 \times 15 = 1500 , \text{cm}^3 \]
- Now, multiply \( 1500 , \text{cm}^3 \) by \( 3.14 \):
\[ 1500 \times 3.14 = 4710 , \text{cm}^3 \]
- Now, divide by \( 3 \):
\[ V = \frac{4710}{3} = 1570 , \text{cm}^3 \]
So, the volume of the cone is:
\[ \boxed{1570} , \text{cubic centimeters} \]