Find the volume of a right circular cone that has a height of 7.4 in and a base with a diameter of 5.4 in. 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, and $h$ is the height of the cone.

1. First, find the radius of the base. The diameter is given as 5.4 inches, so the radius $r$ is half of the diameter:

$r = \frac{5.4}{2} = 2.7 \text{ inches}$

2. The height $h$ is given as 7.4 inches.

3. Substitute the values of $r$ and $h$ into the volume formula:

$V = \frac{1}{3} \pi (2.7)^2 (7.4)$

4. Calculate $(2.7)^2$:

$(2.7)^2 = 7.29$

5. Now, multiply this result by the height $h$:

$7.29 \times 7.4 = 53.946$

6. Finally, multiply by $\frac{1}{3} \pi$:

$V = \frac{1}{3} \pi \times 53.946$

$V = \frac{53.946 \pi}{3}$

$V \approx 17.982 \pi$

7. Using $\pi \approx 3.14159$:

$V \approx 17.982 \times 3.14159$

$V \approx 56.5 \text{ cubic inches}$

So, the volume of the right circular cone is approximately 56.5 cubic inches.