Solution:
1. Given:
- The diameter of the base of the cone is 30 yards.
- The height of the cone is 10 yards.
2. Calculate the radius of the base:
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{30}{2} = 15 \text{ yards}
3. Use the formula for the volume of a cone:
V = \frac{1}{3} \pi r^2 h
4. Substitute the given values into the volume formula:
V = \frac{1}{3} \pi (15)^2 (10)
5. Simplify and calculate the volume:
V = \frac{1}{3} \pi \times 225 \times 10
V = \frac{1}{3} \pi \times 2250
V = 750 \pi \text{ cubic yards}