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 a constant (approximately 3.14 in this case).
First, we need to find the radius. The diameter of the cone is given as 20 cm, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]
Next, we can substitute the values into the volume formula. The height \( h \) is provided as 15 cm.
Now, plugging in the values:
\[ V = \frac{1}{3} \times 3.14 \times (10 , \text{cm})^2 \times 15 , \text{cm \]
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 total:
\[ V = \frac{1}{3} \times 3.14 \times 1500 , \text{cm}^3 \]
Calculating \( 3.14 \times 1500 \):
\[ 3.14 \times 1500 = 4710 \]
Now, divide by 3:
\[ V = \frac{4710}{3} \approx 1570 , \text{cm}^3 \]
So, the volume of the cone is approximately 1570 cm³.