Find the volume of a right circular cone that has a height of 19.2 ft and a base with a circumference of 7.6 ft. 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:
- \( r \) is the radius of the base.
- \( h \) is the height of the cone.

### Step 1: Determine the radius of the base

We know that the circumference of the base is given as 7.6 ft. The formula for the circumference of a circle is:

\[
C = 2 \pi r
\]

Solving for the radius \( r \):

\[
r = \frac{C}{2\pi} = \frac{7.6}{2\pi} \approx 1.21 \text{ ft}
\]

### Step 2: Calculate the volume

Substitute \( r = 1.21 \) ft and \( h = 19.2 \) ft into the volume formula:

\[
V = \frac{1}{3} \pi (1.21)^2 (19.2)
\]

Simplifying:

\[
V = \frac{1}{3} \pi (1.4641)(19.2) \approx \frac{1}{3} \pi (28.12) \approx 29.4 \text{ cubic feet}
\]

Thus, the volume of the cone is approximately **29.4 cubic feet**.

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Would you like to see more details on any specific step? Here are some related questions for further practice:

1. How would the volume change if the radius of the base was doubled?
2. What is the surface area of the cone given the same dimensions?
3. How do you find the slant height of the cone using the given dimensions?
4. If the cone was filled with water, how much would the water weigh (given 1 cubic foot of water weighs about 62.4 lbs)?
5. How does the formula for the volume of a cone compare to that of a cylinder?

**Tip:** Always remember to square the radius before multiplying by the height when using the volume formula for cones.

Find the volume of a right circular cone that has a height of 19.2 ft and a base with a circumference of 7.6 ft. Round your answer to the nearest tenth of a cubic foot.

Learn how to calculate the volume of a right circular cone with a height of 19.2 ft and a base circumference of 7.6 ft. Follow the step-by-step solution using the cone volume formula and the circumference of a circle. Perfect for students in Grades 8-10, this guide explains key concepts like radius, height, and volume calculation.

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