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To find the volume of the hemisphere, we first need to understand that a hemisphere is half of a sphere. The formula for the volume of a sphere is given as:

\[
V = \frac{4}{3} \pi r^3
\]

For a hemisphere, the volume is half of the sphere’s volume, so the formula becomes:

\[
V_{\text{hemisphere}} = \frac{1}{2} \times \frac{4}{3} \pi r^3 = \frac{2}{3} \pi r^3
\]

Given that the radius \(r = 8\) meters, we can now calculate the volume:

\[
V_{\text{hemisphere}} = \frac{2}{3} \pi (8)^3 = \frac{2}{3} \pi \times 512 = \frac{1024}{3} \pi
\]

Using \( \pi \approx 3.1416 \):

\[
V_{\text{hemisphere}} = \frac{1024}{3} \times 3.1416 \approx 1072.33 \text{ cubic meters}
\]

So, the volume of the hemisphere is approximately **1072.3 m³** (rounded to 1 decimal place).

Would you like any further clarification or details?

Here are five related questions you might find interesting:
1. What is the surface area of the hemisphere, including its base?
2. How does the volume change if the radius is doubled?
3. Can you derive the formula for the surface area of a full sphere?
4. What would the volume be if the shape were a quarter sphere instead of a hemisphere?
5. How do you calculate the volume of a spherical cap (a portion of a sphere)?

**Tip:** Always remember that for volumetric calculations involving spheres or hemispheres, both the radius and the constant \( \pi \) play crucial roles.

What is the volume of a hemisphere with a radius of 8 meters? Remember to give the correct units and round your answer to 1 decimal place.

Find the volume of a hemisphere with a radius of 8 meters using the formula for the volume of a sphere. Step-by-step solution provided, along with rounding to 1 decimal place. Suitable for students in Grades 8-10.

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