Cone Slant Height Calculator – Fast & Accurate Results

Cone Slant Height Calculator

This calculator helps you find the slant height of a right circular cone. Just enter the cone's radius and its vertical height, and we'll quickly compute the slant height for you. It's a handy tool for geometry problems, especially when you're working on surface area calculations.

Radius (r)

Enter the radius of the cone's base.

Height (h)

Enter the vertical height of the cone.

Please enter a positive number for the radius.

How it works

This calculator helps you find the slant height of a right circular cone. Just enter the cone's radius and its vertical height, and we'll quickly compute the slant height for you. It's a handy tool for geometry problems, especially when you're working on surface area calculations.

The Formula

The formula for the slant height (l) of a cone is derived from the Pythagorean theorem:
l = √(r² + h²)
Where:
r = radius of the cone's base
h = vertical height of the cone

Worked Example

Finding the Slant Height of a Traffic Cone
Imagine a traffic cone with a base radius of 10 cm and a vertical height of 24 cm. To find its slant height: 1. **Identify the given values:** r = 10 cm, h = 24 cm. 2. **Apply the formula:** l = √(10² + 24²) 3. **Calculate the squares:** l = √(100 + 576) 4. **Add the values:** l = √676 5. **Find the square root:** l = 26 cm So, the slant height of the traffic cone is 26 cm.

Tips, Assumptions & Limitations

Ensure your radius and height are in the same units (e.g., both in cm or both in inches) for a consistent result.
The slant height is always longer than both the radius and the vertical height.
This calculation is often the first step when finding the surface area of a cone.

FAQ

The slant height of a cone is the distance from any point on the circumference of its base to the apex (the tip) of the cone, measured along the surface. It's different from the vertical height, which is measured straight up from the center of the base to the apex.

Slant height is crucial for calculating the lateral surface area (the curved side) of a cone. The formula for lateral surface area is π * r * l, where 'l' is the slant height. Without it, you can't find the surface area accurately.

This calculator is designed for right circular cones, which are cones where the apex is directly above the center of the circular base. Most cones you encounter in school maths are right circular cones.