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, and \( h \) is the height.
Given the diameter of the cone is 20 cm, the radius \( r \) would be:
\[ r = \frac{\text{diameter}}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]
The height \( h \) is given as 15 cm.
Now substitute the values 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 substitute that back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 100 , \text{cm}^2 \times 15 , \text{cm} \]
Next, calculate \( 3.14 \times 100 \):
\[ 3.14 \times 100 = 314 \]
Now substitute that value:
\[ V = \frac{1}{3} \times 314 , \text{cm}^2 \times 15 , \text{cm} \]
Now calculate \( 314 \times 15 \):
\[ 314 \times 15 = 4710 , \text{cm}^3 \]
Finally, divide by 3:
\[ V = \frac{4710 , \text{cm}^3}{3} = 1570 , \text{cm}^3 \]
Thus, the volume of the cone is:
\[ \boxed{1,570} \text{ cubic centimeters} \]
The correct answer is 1. 1,570 cubic centimeters.