What is the volume of a hemisphere with a radius of 6.1 ft, rounded to the nearest tenth of a cubic foot?

To find the volume of a hemisphere with a radius of 6.1 ft, we can use the formula for the volume of a sphere and then take half of that volume, since a hemisphere is half of a sphere.

The formula for the volume of a sphere is: $V = \frac{4}{3} \pi r^3$

First, we calculate the volume of the entire sphere with radius $r = 6.1$ ft: $V = \frac{4}{3} \pi (6.1)^3$

Now, let's compute $(6.1)^3$: $6.1 \times 6.1 \times 6.1 = 226.981$

Next, we multiply this result by $\frac{4}{3} \pi$: $V = \frac{4}{3} \pi \times 226.981$

Using $\pi \approx 3.14159$: $V = \frac{4}{3} \times 3.14159 \times 226.981$ $V \approx \frac{4}{3} \times 712.382$ $V \approx 949.843$

Since we are looking for the volume of a hemisphere, we take half of this volume: $V_{\text{hemisphere}} = \frac{949.843}{2}$ $V_{\text{hemisphere}} \approx 474.9215$

Rounding to the nearest tenth: $V_{\text{hemisphere}} \approx 474.9$

Therefore, the volume of the hemisphere is approximately 474.9 cubic feet.