1. What Is A Hemisphere?

A hemisphere is half of a sphere, created by cutting a sphere along a plane through its center. It has one flat circular face and one curved surface.

2. Hemisphere Volume Formula

The volume of a hemisphere is calculated using:

Where:

• \( V \) — Volume (cubic length units)
• \( \pi \) — Mathematical constant (~3.14159)
• \( r \) — Radius (length units)

Explanation: The formula is derived from the full sphere volume formula \( \frac{4}{3}\pi r^3 \), halved to account for the hemisphere.

3. How The Calculator Works

Calculation Steps: The calculator takes the radius value, cubes it, multiplies by π, then by 2/3 to get the volume.

4. Practical Applications

Examples: Calculating volume of domes, hemispherical tanks, architectural elements, or any half-spherical object.

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use?
A: Use consistent length units (meters, feet, etc.) - the volume will be in cubed units of whatever you input.

Q3: Can I calculate diameter instead of radius?
A: Yes, but you must first divide diameter by 2 to get radius before using the formula.

Q4: What if my hemisphere isn't perfect?
A: This formula assumes a perfect mathematical hemisphere. For irregular shapes, other methods are needed.

Q5: How precise is this calculation?
A: Mathematically exact for perfect hemispheres, limited only by measurement precision of the radius.