Find the volume of a right circular cone that has a height of 2.5 feet and a base with a diameter of 8 feet. Round your answer to the nearest tenth of a cubic foot.

To find the volume of a right circular cone, we use the following formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \(V\) is the volume of the cone,
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.

### Step 1: Identify the given values.
- The height \(h\) is 2.5 feet.
- The diameter of the base is 8 feet, so the radius \(r\) is half of the diameter: 
  \[
  r = \frac{8}{2} = 4 \text{ feet}.
  \]

### Step 2: Substitute the values into the formula.
\[
V = \frac{1}{3} \pi (4)^2 (2.5)
\]

\[
V = \frac{1}{3} \pi (16)(2.5)
\]

\[
V = \frac{1}{3} \pi (40)
\]

\[
V = \frac{40 \pi}{3}
\]

### Step 3: Calculate the value.
Using \(\pi \approx 3.1416\):
\[
V \approx \frac{40 \times 3.1416}{3} \approx \frac{125.664}{3} \approx 41.9 \text{ cubic feet}.
\]

### Final Answer:
The volume of the cone is approximately **41.9 cubic feet**.

Would you like further details or have any questions?

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Here are five related questions for further exploration:
1. What is the surface area of the same cone?
2. How would the volume change if the height were doubled?
3. How do you calculate the volume of a cone with an elliptical base?
4. What is the slant height of the cone given the current dimensions?
5. How does the volume of a cone compare to that of a cylinder with the same base and height?

**Tip**: Remember, the volume of a cone is always one-third that of a cylinder with the same base and height!

Learn how to find the volume of a right circular cone with a height of 2.5 feet and a base diameter of 8 feet. This problem uses key geometry concepts and the cone volume formula V = (1/3)πr²h to provide a detailed solution. Suitable for students in Grades 8-10.

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