To find the volume of the cone, we use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.
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Calculate the radius: The diameter of the cone is given as 30 centimeters, so the radius \( r \) is half of the diameter:
\[ r = \frac{30}{2} = 15 \text{ cm} \]
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Calculate the height: The height \( h \) is twice the length of the diameter. Therefore, the height is:
\[ h = 2 \times 30 = 60 \text{ cm} \]
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Substitute \( r \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \pi (15)^2 (60) \]
First, calculate \( (15)^2 \):
\[ (15)^2 = 225 \]
Now substitute this back into the volume formula:
\[ V = \frac{1}{3} \pi (225) (60) \]
Next, calculate \( 225 \times 60 \):
\[ 225 \times 60 = 13500 \]
Now substitute this into the volume formula:
\[ V = \frac{1}{3} \pi (13500) \]
Finally, calculate \( \frac{13500}{3} \):
\[ \frac{13500}{3} = 4500 \]
Thus, the volume of the cone is:
\[ V = 4500 \pi \text{ cm}^3 \]
If you want it in decimal form, using \( \pi \approx 3.14 \):
\[ V \approx 4500 \times 3.14 \approx 14130 \text{ cm}^3 \]
Thus, the volume of the cone is:
\[ \boxed{4500 \pi \text{ cm}^3} \text{ or approximately } \boxed{14130 \text{ cm}^3} \]