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, from domes to certain fruits.

2. Hemisphere Volume Formula

The volume of a hemisphere is calculated using:

Where:

• \( V \) — Volume (cubic units)
• \( \pi \) — Pi (approximately 3.14159)
• \( r \) — Radius of the hemisphere (linear units)

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

3. How the Calculation Works

Steps:

1. Cube the radius (multiply radius by itself twice)
2. Multiply by π (approximately 3.14159)
3. Multiply by 2/3

4. Practical Applications

Examples: Calculating volume of domes, hemispherical tanks, certain architectural elements, and natural formations.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from a sphere volume?
A: A hemisphere is exactly half the volume 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: Does this work for any hemisphere?
A: Yes, as long as it's a perfect hemisphere (half of a perfect sphere).

Q4: What if I have diameter instead of radius?
A: First divide diameter by 2 to get radius before using the formula.

Q5: How accurate is this formula?
A: It's mathematically exact for perfect hemispheres.