Hemisphere Plus Cylinder Volume

1. Identify the two solids

A hemisphere is half of a sphere, and a cylinder has a circular base and a height. In these problems, find the volume of each solid separately, then add them.

2. Use the volume formulas

• Hemisphere: (V = \frac{2}{3}\pi r^3)
• Cylinder: (V = \pi r^2 h)

Use the same radius for both parts if the diagram shows they fit together.

3. Substitute carefully

1. Read the radius (r) from the figure.
2. Read the cylinder height (h).
3. Replace (r) and (h) in both formulas.
4. Simplify each volume before adding, if possible.

4. Add the volumes

Combine the two results: [ V_{total}=\frac{2}{3}\pi r^3+\pi r^2h ] If the problem asks for a simplified exact answer, leave your result in terms of (\pi) unless told otherwise.

5. Check your work

• Make sure both parts use the correct units cubed.
• Confirm that the radius matches in both formulas.
• If you compute a decimal, it should be reasonable compared with the size of the shape.

A good final answer clearly shows the hemisphere volume, the cylinder volume, and their sum.