Slant Height Calculator
Calculate slant height for cones, pyramids, and triangles using Pythagorean theorem
Calculate Slant Height
Vertical height of the cone
Radius of the circular base
Slant Height Results
Formula used: l = √(h² + r²)
Calculation: l = √(0² + 0²) = 0.00
Shape Analysis
Example Calculation
Right Circular Cone
Given: Height = 12 units, Base radius = 5 units
Formula: l = √(h² + r²)
Calculation: l = √(12² + 5²) = √(144 + 25) = √169 = 13 units
Result: Slant height = 13 units
Right Square Pyramid
Given: Height = 8 units, Base side = 6 units
Formula: l = √(h² + (b/2)²)
Calculation: l = √(8² + 3²) = √(64 + 9) = √73 ≈ 8.54 units
Result: Slant height ≈ 8.54 units
Shape Types
Right Circular Cone
l = √(h² + r²)
Uses height and base radius
Right Square Pyramid
l = √(h² + (b/2)²)
Uses height and base side length
Right Triangle
l = √(h² + b²)
Uses height and base length
Calculation Tips
Slant height is always the hypotenuse of a right triangle
For pyramids, use half the base length in calculations
Elevation angle method uses trigonometry
Slant height is always greater than the height
Understanding Slant Height
What is Slant Height?
Slant height is the distance from the apex (top) of a cone or pyramid to any point on the circumference of the base, measured along the surface. It's the hypotenuse of a right triangle formed by the height and the radius (or half the base length).
Applications
- •Calculating surface area of cones and pyramids
- •Engineering and architectural design
- •Navigation and surveying
- •Angles of elevation calculations
Mathematical Foundation
Pythagorean Theorem: a² + b² = c²
Where c is the slant height (hypotenuse)