1. What is Slant Height?

Slant height (l) is the distance from the base to the apex along the lateral face of a right circular cone. It's important for calculating surface area and other geometric properties of cones.

2. How Does the Calculator Work?

The calculator uses the slant height formula:

Where:

• \( l \) — Slant height (length units)
• \( r \) — Radius of the base (length units)
• \( h \) — Height of the cone (length units)

Explanation: The formula comes from the Pythagorean theorem, where the slant height is the hypotenuse of a right triangle formed by the radius and height.

3. Importance of Slant Height Calculation

Details: Slant height is crucial for determining the lateral surface area of cones (πrl) and is used in various engineering and architectural applications involving conical shapes.

4. Using the Calculator

Tips: Enter the radius and height in the same length units (e.g., cm, inches). Both values must be positive numbers. The result will be in the same units as your input.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used for any cone?
A: This formula works specifically for right circular cones. For oblique cones, the calculation is more complex.

Q2: What's the difference between height and slant height?
A: Height is the perpendicular distance from base to apex, while slant height is the diagonal distance along the cone's side.

Q3: How precise should my measurements be?
A: For most practical purposes, measuring to 2 decimal places is sufficient, though precision depends on your specific application.

Q4: Can I calculate radius if I know slant height and height?
A: Yes, you can rearrange the formula: \( r = \sqrt{l^2 - h^2} \).

Q5: Does this work for truncated cones (frustums)?
A: No, frustums have a different formula for their slant height involving both top and bottom radii.