1. What is Slant Height?

Slant height is the distance from the apex (top) to any point on the perimeter of the base along the lateral surface of a cone or pyramid. It represents the length of the slanted side of the three-dimensional shape.

2. How Does the Calculator Work?

The calculator uses the slant height formula:

Where:

• \( r \) — Base radius (units)
• \( h \) — Vertical height (units)
• \( \sqrt{} \) — Square root function

Explanation: This formula is derived 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: Calculating slant height is essential for determining the lateral surface area of cones and pyramids, construction and manufacturing of conical objects, and solving geometric problems involving three-dimensional shapes.

4. Using the Calculator

Tips: Enter the base radius and vertical height in the same units. Both values must be positive numbers. The calculator will compute the slant height using the Pythagorean relationship.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between height and slant height?
A: Height is the vertical distance from base to apex, while slant height is the diagonal distance along the lateral surface from apex to base edge.

Q2: Can this formula be used for pyramids?
A: Yes, for right pyramids with a regular polygonal base, where r represents the apothem (distance from center to midpoint of a side).

Q3: What units should I use?
A: Use consistent units for all measurements (meters, centimeters, inches, etc.). The result will be in the same units.

Q4: Does this work for oblique cones?
A: No, this formula applies only to right cones and pyramids where the apex is directly above the center of the base.

Q5: How is slant height related to surface area?
A: Lateral surface area of a cone = π × r × slant height, making slant height crucial for surface area calculations.