1. What is a Hemisphere?

A hemisphere is half of a sphere, divided by a plane passing through its center. It's a three-dimensional shape that appears in many natural and man-made objects.

2. Hemisphere Volume Formula

The volume of a hemisphere is calculated using:

Where:

• \( V \) — Volume of the hemisphere (cubic units)
• \( \pi \) — Mathematical constant (~3.14159)
• \( r \) — Radius of the hemisphere (linear units)

Explanation: Since a hemisphere is exactly half of a sphere, its volume is half of the sphere's volume formula \( \frac{4}{3}\pi r^3 \).

3. How to Calculate Volume

Steps:

1. Measure or obtain the radius of the hemisphere
2. Cube the radius (multiply it by itself twice)
3. Multiply by π (approximately 3.14159)
4. Multiply by 2/3

4. Practical Applications

Examples: Calculating volume of domes, hemispherical bowls, architectural elements, or natural formations like certain rock cavities.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from a sphere's volume?
A: A hemisphere's volume is exactly half of a full sphere with the same radius.

Q2: What units should I use?
A: Use consistent units - if radius is in meters, volume will be in cubic meters.

Q3: Can I use diameter instead of radius?
A: Yes, but remember radius = diameter/2, so you'd need to adjust the formula.

Q4: Is this formula exact?
A: Yes, it's mathematically exact assuming perfect hemispherical shape.

Q5: What about surface area?
A: Hemisphere has two surface areas - curved (2πr²) and flat (πr²) - not covered by this calculator.