To find the volume of a hemisphere (which is half of a sphere), we can use the formula for the volume of a sphere and then divide it by 2.
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Since the diameter of the hemisphere is given as 5 cm, we can find the radius by dividing the diameter by 2:
\[ r = \frac{5}{2} = 2.5 \text{ cm} \]
Now we can calculate the volume of the hemisphere by substituting the radius into the sphere volume formula and then taking half of that.
First, calculate the volume of the entire sphere:
\[ V = \frac{4}{3} \pi (2.5)^3 \]
Calculating \( (2.5)^3 \):
\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 6.25 \times 2.5 = 15.625 \]
Now substitute back into the volume formula:
\[ V = \frac{4}{3} \pi (15.625) \]
Calculating \( \frac{4}{3} \times 15.625 \):
\[ \frac{4}{3} \times 15.625 \approx 20.8333333 \]
Thus, the volume of the sphere is:
\[ V \approx 20.8333333 \pi \]
Now, we take half of that to find the volume of the hemisphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \times 20.8333333 \pi \approx 10.41666665 \pi \]
Now, using the value of \( \pi \approx 3.14159265 \), we can approximate:
\[ V_{\text{hemisphere}} \approx 10.41666665 \times 3.14159265 \approx 32.703 \]
Finally, rounding to the nearest hundredth, we get:
\[ \text{Volume of the hemisphere} \approx 32.70 \text{ cm}^3 \]
Thus, the volume of the hemisphere is:
\[ \boxed{32.70} \text{ cm}^3 \]