The problem asks to calculate the volume of a cone with the given height and radius using the formula for the volume of a cone:

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

Given:

• Radius $r = 6$ feet
• Height $h = 3$ feet

Step-by-Step Calculation:

1. Substitute the values of $r$ and $h$ into the formula: $V = \frac{1}{3} \pi (6)^2 (3)$
2. Calculate $6^2$: $6^2 = 36$
3. Now the equation becomes: $V = \frac{1}{3} \pi (36) (3)$
4. Simplify the expression: $V = \frac{1}{3} \pi (108)$
5. Now divide by 3: $V = 36 \pi$
6. Approximate $\pi$ as 3.1416: $V \approx 36 \times 3.1416 = 113.1 \text{ cubic feet}$

Final Answer:

The volume of the cone is approximately 113.1 cubic feet.

Would you like further details on the calculation, or do you have any questions?

Here are 5 related questions to expand on this topic:

1. How does the volume of a cone change if the height is doubled but the radius remains the same?
2. What is the effect on the volume if both the radius and the height are halved?
3. How would the formula for the volume of a cone change if the shape was a cylinder instead?
4. What is the lateral surface area of a cone, and how do you calculate it?
5. Can the volume formula for cones be used for cones with an elliptical base?

Tip: When calculating volumes of three-dimensional shapes, make sure all dimensions are in the same unit system to avoid errors in the result.