1. What is the Base Radius of Cone Formula?

The base radius of a cone can be calculated using the relationship between total surface area and lateral surface area. This formula provides an accurate measurement of the cone's base radius when the surface areas are known.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{Base} \) — Base radius of the cone (m)
• \( TSA \) — Total surface area of the cone (m²)
• \( LSA \) — Lateral surface area of the cone (m²)
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula derives from the relationship TSA = LSA + base area, where base area = πr².

3. Importance of Base Radius Calculation

Details: Calculating the base radius is essential for various geometric calculations, construction projects, and engineering applications involving conical structures.

4. Using the Calculator

Tips: Enter both total surface area and lateral surface area in square meters. Values must be positive numbers, and TSA must be greater than LSA.

5. Frequently Asked Questions (FAQ)

Q1: Why must TSA be greater than LSA?
A: Total surface area includes both lateral surface area and base area, so TSA must always be greater than LSA for any cone.

Q2: What units should I use for input values?
A: The calculator accepts any consistent area units, but results will be in the corresponding length units (e.g., m² input gives m output).

Q3: Can this formula be used for truncated cones?
A: No, this formula is specifically for right circular cones with a single base.

Q4: What if I get an imaginary number result?
A: This indicates that LSA is greater than TSA, which is mathematically impossible for a cone. Check your input values.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values and perfect conical geometry.