Surface Area Formulas Reference Guide

Compare and learn the exact surface area equations for all major 3D geometric shapes: spheres, cubes, cylinders, cones, and hemispheres.

3D Surface Area Formulas Table

3D Solid Shape	Total Surface Area Formula	Lateral / Curved Area	Calculator Link
Sphere	`A = 4πr² = πd²`	4πr² (all curved)	Sphere Area
Cube	`A = 6a²`	4a² (4 side faces)	Cube Area
Cylinder	`A = 2πr(r + h)`	2πrh (curved wall)	Cylinder Area
Cone	`A = πr(r + l)`	πrl (slant cone)	Cone Area
Hemisphere	`A = 3πr²`	2πr² (curved dome)	Hemisphere Area

The Sphere Surface Area: A = 4πr²

The surface area of a sphere is remarkable because it is exactly four times the area of its great circle (\(\pi r^2\)). Furthermore, taking the derivative of the Sphere Volume Formula with respect to radius produces the exact surface area:

\frac{d}{dr}\left(\frac{4}{3}\pi r^3\right) = 4\pi r^2

Frequently Asked Questions

What is the difference between surface area and volume?

Surface area measures the 2D exterior boundary of a 3D object in square units (e.g., cm²). Volume measures the 3D space contained inside the object in cubic units (e.g., cm³).

Which shape has the smallest surface area for a given volume?

A sphere has the minimum surface area of any geometric shape for a fixed volume. This is why bubbles and celestial bodies naturally form spheres.