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,
- \( h \) is the height of the cone.
First, we need to find the radius. The diameter of the cone is 20 cm, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]
Next, we can plug in the values into the volume formula. The height \( h \) is 15 cm, and we will use \( \pi = 3.14 \):
\[ V = \frac{1}{3} \times 3.14 \times (10 , \text{cm})^2 \times 15 , \text{cm} \]
Calculating \( (10 , \text{cm})^2 \):
\[ (10 , \text{cm})^2 = 100 , \text{cm}^2 \]
Now substitute this back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 100 , \text{cm}^2 \times 15 , \text{cm} \]
Calculating \( 100 \times 15 \):
\[ 100 , \text{cm}^2 \times 15 , \text{cm} = 1500 , \text{cm}^3 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 1500 , \text{cm}^3 \]
Calculating \( 3.14 \times 1500 \):
\[ 3.14 \times 1500 = 4710 \]
Now divide by 3:
\[ V = \frac{4710}{3} = 1570 , \text{cm}^3 \]
Thus, the volume of the cone is:
\[ \boxed{1,570 , \text{cubic centimeters}} \]
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