1. What is Slant Height of a Cone?

The slant height (l) of a cone is the distance from the apex to any point on the edge of the circular base. It's different from the vertical height (h) which is the perpendicular distance from the base to the apex.

2. How Does the Calculator Work?

The calculator uses the slant height formula:

Where:

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

Explanation: The formula comes from the Pythagorean theorem, where the slant height forms the hypotenuse of a right triangle with the radius and height as the other two sides.

3. Importance of Slant Height Calculation

Details: Knowing the slant height is essential for calculating the lateral surface area of a cone, which is important in construction, manufacturing, and geometry problems.

4. Using the Calculator

Tips: Enter the radius and height in the same units (e.g., both in cm or both in inches). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: 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.

Q2: Can I use this for truncated cones?
A: No, this formula is only for complete cones. Truncated cones (frustums) have a different formula.

Q3: What units should I use?
A: Any consistent length units (cm, m, inches, etc.) as long as both measurements use the same units.

Q4: How accurate is this calculation?
A: It's mathematically precise, assuming perfect cone geometry and accurate input measurements.

Q5: What if I know slant height and need to find height or radius?
A: You can rearrange the formula: \( h = \sqrt{l^2 - r^2} \) or \( r = \sqrt{l^2 - h^2} \).