To find the volume of the hemisphere, we can start by using the formula for the volume of a sphere and then divide it by 2 since a hemisphere is half of a sphere.
The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
- Determine the radius: The problem states that the diameter of the hemisphere is 5 cm. The radius \( r \) is half of the diameter.
\[ r = \frac{5 , \text{cm}}{2} = 2.5 , \text{cm} \]
- Calculate the volume of the sphere using the radius:
\[ V_{\text{sphere}} = \frac{4}{3} \pi (2.5)^3 \]
- Calculate \( (2.5)^3 \):
\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \]
- Substitute \( (2.5)^3 \) back into the volume formula:
\[ V_{\text{sphere}} = \frac{4}{3} \pi (15.625) \]
- Now calculate \( \frac{4}{3} \times 15.625 \):
\[ \frac{4}{3} \times 15.625 = \frac{62.5}{3} \approx 20.8333 \]
- Now multiply by \( \pi \). Using \( \pi \approx 3.14159 \):
\[ V_{\text{sphere}} \approx 20.8333 \times 3.14159 \approx 65.497 \]
- Since we want the volume of the hemisphere, we divide the volume of the sphere by 2:
\[ V_{\text{hemisphere}} = \frac{65.497}{2} \approx 32.7485 \]
- Round the answer to the nearest hundredth:
\[ V_{\text{hemisphere}} \approx 32.75 , \text{cm}^3 \]
Thus, the volume of the hemisphere, rounded to the nearest hundredth, is \( \boxed{32.75} \) cm³.