https://file.aiquickdraw.com/mathbot/file/173354821696716k6mzil.jpg

To find the volume of the cone, we use the formula:

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

### Given:
- \( r = 5.1 \, \text{in} \)
- \( h = 11.4 \, \text{in} \)
- \( \pi = 3.141592654 \)

### Substituting the values:
\[
V = \frac{1}{3} \cdot 3.141592654 \cdot (5.1)^2 \cdot 11.4
\]

First, calculate \( r^2 \):
\[
5.1^2 = 26.01
\]

Now, multiply by \( h \):
\[
26.01 \cdot 11.4 = 296.514
\]

Next, multiply by \( \pi \):
\[
296.514 \cdot 3.141592654 = 931.700728
\]

Finally, divide by 3:
\[
V = \frac{931.700728}{3} = 310.6 \, \text{cubic inches (rounded to the nearest tenth)}.
\]

### Final Answer:
The volume of the cone is **310.6 cubic inches**.

Would you like more details or further clarifications?

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### Related Questions:
1. How does the cone's volume change if the height doubles but the radius remains the same?
2. What is the surface area of this cone, including its base?
3. How would the volume formula change if the shape were a pyramid instead of a cone?
4. What are the units for the final answer, and why are they cubic inches?
5. How does the precision of \( \pi \) (e.g., using \( \pi \approx 3.14 \)) affect the result?

### Tip:
When working with \( \pi \), always decide the level of precision required based on the context (e.g., using \( 3.14 \) for quick estimates or full precision for exact results).

Find the volume of a right circular cone that has a height of 11.4 in and a base with a radius of 5.1 in. Round your answer to the nearest tenth of a cubic inch. Use π as 3.141592654.

Learn how to calculate the volume of a right circular cone with a radius of 5.1 inches and a height of 11.4 inches. This step-by-step solution uses the formula V = (1/3)πr²h with π approximated to 3.141592654, providing the final volume rounded to the nearest tenth of a cubic inch.

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