1. What Is Slant Height?

Slant height is the distance from the apex (top) of a cone to any point on the circumference of its base, measured along the lateral surface. It represents the true length of the side of a cone, as opposed to the vertical height.

2. How Does The Calculator Work?

The calculator uses the Pythagorean theorem formula:

Where:

• \( \text{Height} \) — Vertical height from base to apex (m)
• \( \text{Radius} \) — Radius of the circular base (m)
• \( \text{Slant Height} \) — Diagonal distance along the lateral surface (m)

Explanation: This formula derives from the Pythagorean theorem, treating the slant height as the hypotenuse of a right triangle formed by the height, radius, and slant height.

3. Importance Of Slant Height Calculation

Details: Slant height is crucial for calculating the lateral surface area of cones, determining material requirements for conical structures, and solving geometric problems involving three-dimensional shapes.

4. Using The Calculator

Tips: Enter the vertical height and radius of the cone in meters. Both values must be positive numbers. The calculator will compute the slant height using the Pythagorean theorem.

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: No, this specific formula applies only to right circular cones. Pyramids have different formulas depending on their base shape.

Q3: What units should I use?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.).

Q4: How is slant height used in real-world applications?
A: Used in construction (conical roofs), manufacturing (cone-shaped objects), packaging, and architectural design.

Q5: What if I have diameter instead of radius?
A: Divide the diameter by 2 to get the radius before using the calculator.