Find the volume of a right circular cone that has a height of 18.4 inches and a base with a circumference of 9.3 inches. Round your answer to the nearest tenth of a cubic inch.

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

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

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

### Step 1: Find the radius \( r \)
We are given the circumference of the base \( C = 9.3 \) inches. The formula for the circumference of a circle is:

\[
C = 2 \pi r
\]

Solving for \( r \):

\[
r = \frac{C}{2 \pi} = \frac{9.3}{2 \pi} \approx \frac{9.3}{6.2832} \approx 1.48 \, \text{inches}
\]

### Step 2: Use the volume formula
Now that we have \( r \approx 1.48 \) inches and \( h = 18.4 \) inches, we can plug these values into the volume formula:

\[
V = \frac{1}{3} \pi (1.48)^2 (18.4)
\]

First, calculate \( r^2 \):

\[
1.48^2 \approx 2.19
\]

Now calculate the volume:

\[
V = \frac{1}{3} \pi (2.19) (18.4) \approx \frac{1}{3} \pi (40.296) \approx \frac{1}{3} (126.526) \approx 42.175
\]

### Step 3: Round the answer
Rounding to the nearest tenth, the volume of the cone is approximately:

\[
\boxed{42.2} \, \text{cubic inches}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you calculate the surface area of a right circular cone?
2. What is the difference between a right circular cone and an oblique cone?
3. How would the volume change if the base radius doubled?
4. How does the height affect the volume of a cone?
5. How is the volume formula for a cone related to that of a cylinder?

### Tip:
Always check units in geometry problems to ensure that you're working consistently in one system (e.g., inches, feet, meters).

Learn how to find the volume of a right circular cone with a height of 18.4 inches and a base circumference of 9.3 inches. This step-by-step guide uses geometry formulas to solve the problem and provides a clear explanation suitable for Grades 8-10 students.

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