To find the volume of the cone, we use the formula for the volume of a cone, which is:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
Given that the diameter of the cone is 30 centimeters, we can find the radius:
\[ r = \frac{\text{diameter}}{2} = \frac{30}{2} = 15 \text{ cm} \]
The problem states that the height of the cone is twice the length of the diameter. Since the diameter is 30 cm, the height can be calculated as follows:
\[ h = 2 \times \text{diameter} = 2 \times 30 = 60 \text{ cm} \]
Now we can substitute \( r \) and \( h \) into the volume formula:
\[ V = \frac{1}{3} \pi (15)^2 (60) \]
Calculating \( (15)^2 \):
\[ (15)^2 = 225 \]
Now substitute back into the volume formula:
\[ V = \frac{1}{3} \pi (225)(60) \]
Now calculate \( 225 \times 60 \):
\[ 225 \times 60 = 13500 \]
Substituting this back, we have:
\[ V = \frac{1}{3} \pi (13500) \]
Now divide \( 13500 \) by \( 3 \):
\[ V = 4500 \pi \]
Therefore, the volume of the cone is:
\[ \boxed{4500 \pi \text{ cm}^3} \]