Surface Area of a Cylinder Calculator
Calculate total, lateral, and base surface area of a cylinder with step-by-step solutions
Calculate Cylinder Surface Area
Distance from center to edge of base
Distance between the two bases
Cylinder Surface Area Formulas
Base Surface Area: A_base = 2πr² (two circular bases)
Lateral Surface Area: A_lateral = 2πrh (curved surface)
Total Surface Area: A_total = 2πr² + 2πrh = 2πr(r + h)
Volume: V = πr²h
Example Calculations
Example 1: From Radius
Given: radius = 2 cm, height = 3 cm
Base area: 2π(2²) = 25.13 cm²
Lateral area: 2π(2)(3) = 37.7 cm²
Total area: 25.13 + 37.7 = 62.83 cm²
Example 2: From Diameter
Given: diameter = 10 cm, height = 5 cm
Radius: 10 / 2 = 5 cm
Base area: 2π(5²) = 157.08 cm²
Total area: 157.08 + 157.08 = 314.16 cm²
Quick Reference
Key Formulas
Base Area = 2πr²
Lateral Area = 2πrh
Total Area = 2πr(r + h)
Volume = πr²h
Relationships
r = d / 2
C = 2πr
Lateral area = C × h
Cylinder Components
Quick Tips
Cylinder has 2 circular bases and 1 curved surface
Lateral area is base circumference × height
Total area = 2 base areas + lateral area
Can find height if total surface area is known
Understanding Cylinder Surface Area
What is a Cylinder?
A cylinder is a 3D shape with two parallel circular bases connected by a curved surface. A right circular cylinder has bases that are directly above each other, making it the most common type of cylinder.
Surface Area Components
A cylinder's surface area consists of three parts: two identical circular bases and one lateral (curved) surface. When unfolded, it forms two circles and one rectangle.
Deriving the Formula
Step 1: Base Area
Two circular bases: 2 × πr²
Step 2: Lateral Area
Rectangle: circumference × height = 2πrh
Step 3: Total Area
2πr² + 2πrh = 2πr(r + h)
Real-World Applications
Manufacturing:
Calculate material needed for cylindrical containers, pipes, and tanks
Painting:
Determine paint coverage for cylindrical structures like pillars
Architecture:
Design cylindrical buildings and calculate surface materials