1. What is the Cone Radius Formula?

The cone radius formula calculates the base radius of a right circular cone using the slant height and semi-vertical angle. This relationship is fundamental in geometry and has applications in various engineering and design fields.

2. How Does the Calculator Work?

The calculator uses the cone radius formula:

Where:

• \( r \) — Base radius of the cone
• \( l \) — Slant height of the cone
• \( \theta \) — Semi-vertical angle (angle between axis and slant height)

Explanation: The formula derives from the right triangle formed by the cone's axis, radius, and slant height, using basic trigonometric relationships.

3. Importance of Radius Calculation

Details: Knowing the base radius is essential for calculating the cone's volume, surface area, and for practical applications like manufacturing cones or conical sections.

4. Using the Calculator

Tips: Enter slant height in any length units and semi-vertical angle in degrees. The angle should be between 0 and 90 degrees for a valid cone.

5. Frequently Asked Questions (FAQ)

Q1: What is a semi-vertical angle?
A: It's the angle between the cone's central axis and its slant height (side). For a right circular cone, this angle is less than 90 degrees.

Q2: Can I use this for oblique cones?
A: No, this formula only applies to right circular cones where the apex is directly above the center of the base.

Q3: What if I know the height instead of slant height?
A: You would need to use the Pythagorean theorem: \( l = \sqrt{r^2 + h^2} \), where h is the vertical height.

Q4: How precise should my angle measurement be?
A: For most practical purposes, 1-2 decimal places is sufficient, but more precision may be needed for specialized applications.

Q5: Can I use radians instead of degrees?
A: The calculator currently uses degrees, but you could modify the formula to accept radians if needed.