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

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

where:

• $r$ is the radius of the base of the cone,
• $h$ is the height of the cone.

Step 1: Find the radius

The diameter of the base is 5.8 inches, so the radius is half of that:

$r = \frac{5.8}{2} = 2.9 \text{ inches}$

Step 2: Plug in the values

Now, substitute the radius $r = 2.9$ inches and height $h = 3.2$ inches into the formula:

$V = \frac{1}{3} \pi (2.9)^2 (3.2)$

Step 3: Simplify the calculation

First, calculate $(2.9)^2$:

$(2.9)^2 = 8.41$

Now, multiply by $3.2$:

$8.41 \times 3.2 = 26.912$

Now, multiply by $\pi$ (approximately 3.1416):

$26.912 \times 3.1416 = 84.533$

Finally, divide by 3:

$\frac{84.533}{3} = 28.2$

Final Answer:

The volume of the cone is approximately 28.2 cubic inches.

Would you like to see more details on this calculation or have any other questions?

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Here are some related questions you might find interesting:

1. How does the volume change if the radius is doubled while keeping the height constant?
2. What is the surface area of a right circular cone?
3. How would the volume formula change for a cone with a slant height given instead of the height?
4. How do you calculate the volume of a cone when you only know the slant height and radius?
5. How does the volume of a cone compare to the volume of a cylinder with the same radius and height?

Tip: Always remember that the volume of a cone is one-third of the volume of a cylinder with the same base and height!