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 of a sphere \( V \) is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Step 1: Find the radius
The diameter of the hemisphere is given as 5 cm, so we can calculate the radius \( r \) as:
\[ r = \frac{\text{diameter}}{2} = \frac{5 \text{ cm}}{2} = 2.5 \text{ cm} \]
Step 2: Calculate the volume of the sphere
Now, we can plug the radius into the volume formula for a sphere:
\[ V = \frac{4}{3} \pi (2.5)^3 \]
First, calculate \( (2.5)^3 \):
\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \]
Now substitute this back into the volume formula:
\[ V = \frac{4}{3} \pi (15.625) \]
Calculating \( \frac{4}{3} \times 15.625 \):
\[ \frac{4 \times 15.625}{3} = \frac{62.5}{3} \approx 20.8333 \]
Thus, the volume of the whole sphere is approximately:
\[ V \approx 20.8333 \pi \]
Step 3: Calculate the volume of the hemisphere
To find the volume of the hemisphere, we take half of the volume of the sphere:
\[ \text{Volume of the hemisphere} = \frac{1}{2} \times 20.8333 \pi \approx 10.41665 \pi \]
Step 4: Approximate the volume using \( \pi \approx 3.14159 \)
We can now calculate this expression:
\[ 10.41665 \pi \approx 10.41665 \times 3.14159 \approx 32.7496 \]
Step 5: Round to the nearest hundredth
Finally, rounding \( 32.7496 \) to the nearest hundredth gives:
\[ \text{Volume of the hemisphere} \approx 32.75 , \text{cm}^3 \]
Thus, the volume of the hemisphere of ice cream is approximately 32.75 cm³.
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