1. What is the Base Radius of Cone Formula?

The base radius of a cone can be calculated using the Pythagorean theorem when the slant height and vertical height are known. This formula helps determine the radius of the circular base of a right circular cone.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{Base} \) — Base radius of the cone (m)
• \( h_{Slant} \) — Slant height of the cone (m)
• \( h \) — Vertical height of the cone (m)

Explanation: This formula is derived from the Pythagorean theorem applied to the right triangle formed by the height, radius, and slant height of the cone.

3. Importance of Base Radius Calculation

Details: Calculating the base radius is essential for determining the cone's volume, surface area, and other geometric properties. It's crucial in engineering, architecture, and various mathematical applications.

4. Using the Calculator

Tips: Enter the slant height and vertical height in meters. Both values must be positive, and the slant height must be greater than the vertical height for a valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why must the slant height be greater than the height?
A: In a right circular cone, the slant height is always greater than the vertical height due to the Pythagorean relationship between the three dimensions.

Q2: What units should I use for the inputs?
A: The calculator accepts any consistent units, but meters are recommended. Ensure both measurements use the same units.

Q3: Can this formula be used for oblique cones?
A: No, this formula applies only to right circular cones where the apex is directly above the center of the base.

Q4: What if I get a negative value under the square root?
A: This indicates invalid input where the slant height is not greater than the vertical height, which is geometrically impossible for a right circular cone.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, but the precision depends on the accuracy of your input measurements.