Radius of a Cylinder Calculator
Calculate the radius of a cylinder using various geometric parameters and formulas
Calculate Cylinder Radius
The height of the cylinder
The volume of the cylinder
Calculation Results
Formula used: r = √(V / (π × h))
Calculation Analysis
Example Calculation
Water Tank Example
Problem: A cylindrical water tank has a volume of 500 liters and height of 2 meters
Given: Volume = 0.5 m³, Height = 2 m
Find: Radius of the tank
Solution
Using formula: r = √(V / (π × h))
r = √(0.5 / (π × 2))
r = √(0.5 / 6.283)
r = √(0.0796)
r = 0.282 meters
Cylinder Formulas
Volume
V = π × r² × h
Base Area
A_b = 2 × π × r²
Lateral Area
A_l = 2 × π × r × h
Total Surface Area
A = A_b + A_l
Diagonal
d = √(4r² + h²)
Calculator Tips
Choose the method based on known parameters
Ensure all input values use consistent units
Radius is half the diameter of the base
Base area includes both top and bottom circles
Diagonal is the longest distance in the cylinder
Understanding Cylinder Radius Calculations
What is a Cylinder Radius?
The radius of a cylinder is the distance from the center of the circular base to any point on the circumference. It's a fundamental measurement that determines all other properties of the cylinder including volume, surface area, and capacity.
Key Properties
- •Radius determines the circular cross-section
- •Diameter equals twice the radius
- •Volume increases with the square of radius
- •Surface area depends on both radius and height
Common Applications
- •Engineering design and manufacturing
- •Tank and pipe capacity calculations
- •Architecture and construction
- •Material science and physics
Pro Tip: When working with real-world problems, always verify that your calculated radius makes physical sense given the context and constraints.
Formula Derivations
From Volume and Height
V = π × r² × h
r² = V / (π × h)
r = √(V / (π × h))
From Lateral Area and Height
A_l = 2 × π × r × h
r = A_l / (2 × π × h)