1. What is the Cone Radius Formula?

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

2. How Does the Calculator Work?

The calculator uses the cone radius formula:

Where:

• \( r \) — Radius of the cone's base (m)
• \( V \) — Volume of the cone (m³)
• \( h \) — Height of the cone (m)
• \( \pi \) — Pi constant (~3.14159)

Explanation: The formula is derived by rearranging 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 in various engineering, architectural, and manufacturing applications where cone-shaped objects are designed or analyzed.

4. Using the Calculator

Tips: Enter the volume in cubic meters (m³) and height in meters (m). Both values must be positive numbers. The calculator will compute the base radius in meters.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for oblique cones?
A: No, this formula is specifically for right circular cones where the apex is directly above the center of the base.

Q2: What units should I use?
A: The calculator uses meters, but any consistent unit system will work as long as volume and height are in compatible units.

Q3: How accurate is the calculation?
A: The calculation is mathematically precise, but practical accuracy depends on the precision of your input measurements.

Q4: Can I calculate height if I know volume and radius?
A: Yes, you can rearrange the formula to \( h = \frac{3V}{\pi r^2} \).

Q5: What if my cone is truncated?
A: This formula doesn't apply to frustums (truncated cones). You would need different formulas that account for both top and bottom radii.