To find the volume of the cone, we first need to gather the dimensions:
- Diameter of the cone = 30 cm
- Radius (r) = Diameter / 2 = 30 cm / 2 = 15 cm
- Height (h) = 2 × Diameter = 2 × 30 cm = 60 cm
The formula for the volume \( V \) of a cone is:
\[ V = \frac{1}{3} \pi r^2 h \]
Now, substituting the values into the formula:
\[ V = \frac{1}{3} \pi (15 \text{ cm})^2 (60 \text{ cm}) \]
Calculating \( (15 \text{ cm})^2 \):
\[ (15 \text{ cm})^2 = 225 \text{ cm}^2 \]
Now substituting this back into the volume formula:
\[ V = \frac{1}{3} \pi (225 \text{ cm}^2)(60 \text{ cm}) \]
Calculating the product:
\[ 225 \times 60 = 13500 \]
Now plug this back into the volume equation:
\[ V = \frac{1}{3} \pi (13500 \text{ cm}^3) \]
Calculating \( \frac{13500}{3} \):
\[ \frac{13500}{3} = 4500 \]
Thus, we have:
\[ V = 4500 \pi \text{ cm}^3 \]
So, the volume of the cone is:
4,500π cm³
The correct response is:
4,500π cm3