Skip to main content

Topic

Surface area of 3-dimensional shapes

My Progress

Pug Score

0%

Study Points

+0

Unlock Full Access
Adaptive practice
Video lessons

Read

Surface Area of 3D Shapes

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.

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 common solids A reference table. Rectangular prism surface area equals 2 times (length times width plus width times height plus length times height). Cylinder equals 2 pi r squared plus 2 pi r h. Cone equals pi r squared plus pi r l. Sphere equals 4 pi r squared. SolidSurface area formula Rectangular prism2(lw + wh + lh) Cylinder2πr² + 2πrh Coneπr² + πrl Sphere4πr²
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.

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 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.

Related lessons