The surface area of a 3D shape is the total area of all its faces and surfaces, measured in square units. Learn the surface area formulas for rectangular prisms, cylinders, cones, and spheres, what each variable means, and how unfolding a solid into a net makes the total easy to find.
What surface area means
The surface area of a 3D shape is the total area of all its faces or curved surfaces added together — the amount of material it would take to wrap the solid with no gaps or overlaps. It is measured in square units.
Surface area formulas
Each solid has its own formula, but they all add up the areas of the surfaces that make up the shape.
Surface area formulas for a rectangular prism, cylinder, cone, and sphere.
Here r is the radius, h the height, l the slant height, and l, w, h the length, width, and height of a prism.
Using a net
A quick way to see a surface-area formula is to unfold the solid into a flat net. Every face becomes a flat region whose area you already know, and the surface area is simply their sum — the idea behind the surface area of prisms.
Surface area vs volume
Surface area measures the outside (in square units); volume measures the space inside (in cubic units). Many lessons pair them, such as the surface area and volume of cylinders.