1. What is the Volume of Hemisphere Formula?

The volume of a hemisphere can be calculated from its curved surface area using the formula: \[ V = \frac{2}{3} \pi \left( \frac{CSA}{2\pi} \right)^{\frac{3}{2}} \] This formula allows you to determine the volume when you know the curved surface area of the hemisphere.

2. How Does the Calculator Work?

The calculator uses the hemisphere volume formula:

Where:

• \( V \) — Volume of Hemisphere (m³)
• \( CSA \) — Curved Surface Area of Hemisphere (m²)
• \( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula derives the radius from the curved surface area and then calculates the volume using the standard hemisphere volume formula.

3. Importance of Volume Calculation

Details: Calculating the volume of a hemisphere is important in various engineering, architectural, and scientific applications where hemispherical shapes are used, such as domes, tanks, and structural components.

4. Using the Calculator

Tips: Enter the curved surface area in square meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between a hemisphere and a sphere?
A: A hemisphere is exactly half of a sphere, divided along a plane through its center.

Q2: Can this formula be used for any hemisphere?
A: Yes, this formula applies to all perfect hemispheres where the curved surface area is known.

Q3: What are the units for the result?
A: The volume is calculated in cubic meters (m³) when the input is in square meters (m²).

Q4: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values and the formula.

Q5: Can I use this for partial hemispheres?
A: No, this formula is specifically for complete hemispheres. Partial hemispheres require different calculations.