What is the volume of a hemisphere with a radius of 3.6 cm, rounded to the nearest tenth of a cubic centimeter?

To find the volume of a hemisphere, we use the formula for the volume of a sphere and then divide by 2, since a hemisphere is half of a sphere. The formula for the volume of a sphere is:

$V = \frac{4}{3} \pi r^3$

Given that the radius $r$ is 3.6 cm, we first calculate the volume of the sphere:

$V = \frac{4}{3} \pi (3.6)^3$

First, calculate $(3.6)^3$:

$3.6 \times 3.6 = 12.96$ $12.96 \times 3.6 = 46.656$

So,

$V = \frac{4}{3} \pi \times 46.656$

Next, multiply $\frac{4}{3}$ by 46.656:

$\frac{4}{3} \times 46.656 = 62.208$

Thus,

$V = 62.208 \pi$

Now, to find the volume of the hemisphere, we divide this result by 2:

$V_{\text{hemisphere}} = \frac{62.208 \pi}{2} = 31.104 \pi$

Finally, we approximate $\pi$ as 3.14 and calculate:

$V_{\text{hemisphere}} \approx 31.104 \times 3.14 = 97.26816$

Rounded to the nearest tenth, the volume of the hemisphere is:

$97.3 \, \text{cubic centimeters}$