1. What is the Height of Frustum of Cone given Slant Height?

The height of a frustum of a cone given the slant height is the perpendicular distance between the two parallel bases of the frustum, calculated using the slant height and the difference between the top and bottom radii.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of the frustum
• \( l \) — Slant height of the frustum
• \( R \) — Top radius of the frustum
• \( r \) — Bottom radius of the frustum

Explanation: The formula is derived from the Pythagorean theorem applied to the right triangle formed by the height, slant height, and the difference in radii.

3. Importance of Height Calculation

Details: Calculating the height of a frustum is essential in geometry and various engineering applications, including volume and surface area calculations for conical structures.

4. Using the Calculator

Tips: Enter the slant height, top radius, and bottom radius. All values must be positive numbers, and the slant height must be greater than the absolute difference between the radii.

5. Frequently Asked Questions (FAQ)

Q1: What is a frustum of a cone?
A: A frustum of a cone is the portion of a cone that remains after cutting off the top by a plane parallel to the base.

Q2: Can the height be negative?
A: No, height is always a positive value representing a physical distance.

Q3: What units should I use?
A: Use consistent units for all measurements (e.g., all in meters or all in inches).

Q4: What if the slant height is less than the difference in radii?
A: This would result in an imaginary number, indicating that such a frustum cannot exist with the given dimensions.

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