Find the volume of a right circular cone that had a height of 9.5 inches and a base with a circumference of 3.4 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 of the cone,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.

### Step 1: Find the radius of the base
The problem gives us the circumference of the base as \( 3.4 \) inches. The formula for the circumference of a circle is:

\[
C = 2 \pi r
\]

Solving for \( r \) (the radius):

\[
r = \frac{C}{2 \pi} = \frac{3.4}{2 \pi}
\]

\[
r \approx \frac{3.4}{6.2832} \approx 0.541 \, \text{inches}
\]

### Step 2: Calculate the volume
Now that we know the radius and the height, we can substitute them into the volume formula:

\[
V = \frac{1}{3} \pi (0.541)^2 (9.5)
\]

\[
V \approx \frac{1}{3} \pi (0.292) (9.5) \approx \frac{1}{3} \times 3.1416 \times 2.7737 \approx 2.904 \, \text{cubic inches}
\]

### Final Answer:
The volume of the cone is approximately \( 2.9 \) cubic inches.

Would you like a more detailed explanation or have any questions?

Here are five related questions to deepen your understanding:
1. What is the volume formula for a cylinder?
2. How does changing the radius affect the volume of a cone?
3. If the height of the cone is doubled, how does the volume change?
4. How do you calculate the surface area of a cone?
5. What would happen to the volume if the base circumference were halved?

**Tip:** Always verify that the units of all measurements (such as radius and height) are consistent before solving geometric problems.

Learn how to calculate the volume of a right circular cone with a height of 9.5 inches and a base circumference of 3.4 inches. This problem involves the relationship between circumference and radius, as well as the formula for the volume of a cone. Suitable for students in Grades 8-10.

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