To find the volume of the cone, we can 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 of the cone.
- Find the radius: The diameter of the cone is 30 cm, so the radius \( r \) is half of that:
\[ r = \frac{30 \text{ cm}}{2} = 15 \text{ cm} \]
- Find the height: The problem states that the height of the cone is twice the length of the diameter. Since the diameter is 30 cm, the height \( h \) is:
\[ h = 2 \times \text{diameter} = 2 \times 30 \text{ cm} = 60 \text{ cm} \]
- Calculate the volume: Now substitute the radius and height into the volume formula:
\[ V = \frac{1}{3} \pi (15 \text{ cm})^2 (60 \text{ cm}) \]
Calculating \( (15 \text{ cm})^2 \):
\[ (15)^2 = 225 \text{ cm}^2 \]
Now substituting back into the volume formula:
\[ V = \frac{1}{3} \pi \cdot 225 \text{ cm}^2 \cdot 60 \text{ cm} \]
Calculating \( 225 \times 60 \):
\[ 225 \times 60 = 13500 \]
Now dividing by 3:
\[ V = \frac{13500}{3} \pi \text{ cm}^3 = 4500 \pi \text{ cm}^3 \]
Thus, the volume of the cone is:
\[ \boxed{4500\pi \text{ cm}^3} \]
So the correct response is: 4,500π cm³.