Surface Area Calculator - 3D Shape Areas
Calculate the surface area of 3D shapes: cube, sphere, cylinder, cone, prism, and more. Shows formula and step-by-step calculation with labeled diagrams.
Formula
Depends on shape
Surface area is the sum of the areas of all outer surfaces of a 3D object.
Worked Examples
Example 1: Cylinder
Problem:r=5, h=10
Solution:2π(5)(5+10) = 150π ≈ 471.24
Result:471.24
Example 2: Sphere
Problem:r=3
Solution:4π(3)² = 36π ≈ 113.10
Result:113.10
Frequently Asked Questions
What is the difference between lateral and total surface area?
Lateral area excludes the top and bottom bases (like the label on a soup can). Total area includes all surfaces.
Why is surface area important?
It determines how much material is needed to cover an object (e.g., paint, wrapping paper) or how quickly an object heats up or cools down.
Does volume affect surface area?
Generally, yes, but two objects can have the same volume but very different surface areas (e.g., a flat sheet vs. a cube).
What is the surface area formula for a cube?
For a cube with side length s, Area = 6s².