1. What is the Cone Radius Formula?

The cone radius formula calculates the radius of a right circular cone when you know its volume and height. It's derived from the volume formula of a cone and solves for the radius.

2. How Does the Calculator Work?

The calculator uses the cone radius formula:

Where:

• \( r \) — Radius of the cone's base
• \( V \) — Volume of the cone
• \( h \) — Height of the cone
• \( \pi \) — Pi (approximately 3.14159)

Explanation: The formula rearranges the standard cone volume formula \( V = \frac{1}{3}\pi r^2 h \) to solve for radius.

3. Importance of Radius Calculation

Details: Knowing the radius of a cone is essential for various applications in geometry, engineering, and design, particularly when working with conical shapes where volume and height are known but radius needs to be determined.

4. Using the Calculator

Tips: Enter the volume in cubic units and height in length units. Both values must be positive numbers. The calculator will compute the radius in the same length units as the height.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for all types of cones?
A: This formula works only for right circular cones (cones with a circular base where the apex is directly above the center of the base).

Q2: What units should I use?
A: Use consistent units - volume in cubic units (e.g., cm³) and height in length units (e.g., cm). The radius will be in the same length units as the height.

Q3: Can I use this for truncated cones?
A: No, this formula is only for complete cones. Truncated cones (frustums) require different calculations involving both top and bottom radii.

Q4: How precise is the calculation?
A: The calculator uses precise values of π and provides results rounded to 4 decimal places for practical use.

Q5: What if I know diameter instead of radius?
A: The calculator gives radius. If you need diameter, simply multiply the radius by 2.