1. What is a Hemisphere?

A hemisphere is half of a sphere, created by cutting a sphere along a plane through its center. It's a three-dimensional shape with a curved surface and a flat circular base.

2. Volume Formula Explanation

The volume of a hemisphere is calculated using:

Where:

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

Explanation: The formula is derived from the volume of a full sphere (\( \frac{4}{3}\pi r^3 \)) divided by 2.

3. Practical Applications

Details: Hemisphere volume calculations are used in architecture (domes), engineering (tank design), and physics (fluid dynamics).

4. Using the Calculator

Tips: Enter the radius in any length unit (meters, feet, etc.). The result will be in corresponding cubic units. Ensure radius is positive.

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 if I have the diameter instead of radius?
A: First divide the diameter by 2 to get the radius before using the calculator.

Q3: Can I use this for partial hemispheres?
A: No, this formula only works for exact hemispheres. Other formulas are needed for spherical caps or segments.

Q4: What units should I use?
A: Any consistent length unit can be used (meters, feet, inches). The volume will be in corresponding cubic units.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming perfect hemispherical shape and precise radius measurement.