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.
What is the surface area of a sphere?
Area = 4πr². It is exactly four times the area of a circle with the same radius.
How do I find surface area of irregular shapes?
You divide the object's surface into simpler shapes (triangles, rectangles) and add their areas together.
What is a "Net" in geometry?
A net is a 2D pattern that can be folded to form a 3D shape. Calculating the area of the net gives the surface area of the 3D shape.
Why do biological cells maximize surface area?
Cells need a large surface area to volume ratio to efficiently exchange nutrients and waste with their environment.
How does surface area relate to cooling?
Objects with larger surface area dissipate heat faster. This is why car radiators have fins.
Which shape has the minimum surface area for a given volume?
The sphere has the smallest surface area for any given volume, which is why bubbles are spherical.