Height of a Cone Calculator
Calculate the height of a cone using radius and slant height or volume
Calculate Cone Height
⚠️ Radius must be positive
Cone Height Formulas
Method 1: Using Slant Height and Radius
This formula comes from the Pythagorean theorem applied to the cone's cross-section.
Where: h = height, l = slant height, r = radius
Method 2: Using Volume and Radius
This formula is derived from the cone volume formula: V = (1/3)πr²h
Where: h = height, V = volume, r = radius
Quick Examples
Example 1: Traffic Cone
Radius: 15 cm
Slant Height: 35 cm
Height: 31.62 cm
Example 2: Ice Cream Cone
Radius: 3 cm
Volume: 50 cm³
Height: 5.31 cm
Key Concepts
Right Circular Cone: Apex directly above base center
Slant Height: Distance from apex to base edge
Height: Perpendicular distance from apex to base
Constraint: Slant height must be greater than radius
Understanding Cone Height Calculations
What is a Cone?
A cone is a three-dimensional geometric shape with a circular base and a single vertex called the apex. The height of a cone is the perpendicular distance from the apex to the center of the base.
Types of Cones
- •Right Circular Cone: Apex directly above the base center
- •Oblique Cone: Apex not directly above the base center
Real-World Applications
Traffic Management
Calculate dimensions for traffic cones and safety equipment.
Food Industry
Design ice cream cones, funnels, and packaging containers.
Architecture
Calculate volumes and materials for conical roofs and structures.
Important Relationships
Pythagorean Theorem
l² = h² + r²
Relates height, radius, and slant height
Volume Formula
V = (1/3)πr²h
Volume depends on base area and height
Surface Area
A = πr(r + l)
Total surface area including base