1. What is a Truncated Cone?

A truncated cone (or frustum of a cone) is a cone with the top cut off by a plane parallel to the base. The angle (α) refers to the angle between the side of the cone and its base.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of the truncated cone (m)
• \( R \) — Radius of the base (m)
• \( r \) — Radius of the top (m)
• \( \alpha \) — Angle between side and base (degrees)

Explanation: The formula calculates the height based on the difference in radii and the angle of the cone's side.

3. Importance of Angle in Calculation

Details: The angle determines how steeply the sides of the cone slope. A steeper angle (larger α) results in a taller cone for the same radius difference.

4. Using the Calculator

Tips: Enter all measurements in meters. The top radius (r) must be less than the base radius (R). The angle must be between 0 and 90 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What if my top radius is larger than the base radius?
A: The calculator assumes R > r. If r > R, the cone would be upside down and the formula wouldn't apply.

Q2: What happens at α = 0° or α = 90°?
A: At 0° you'd have an infinite height cylinder. At 90° you'd have a flat disk. Both are edge cases not handled by this calculator.

Q3: Can I use other units besides meters?
A: Yes, as long as all length measurements use the same unit (e.g., all in cm or all in inches).

Q4: How accurate is this calculation?
A: It's mathematically exact for perfect cones. Real-world objects may have imperfections.

Q5: What if I know the height but need to find the angle?
A: You can rearrange the formula: α = arctan(h/(R - r)).