Geometry · Quick Reference

Surface Area Cheat Sheet

Geometry · Lesson 12/16

In one line: surface area measures the total area covering the outside of a three-dimensional solid — essentially the area you'd need to wrap the entire object in paper.

Key Ideas

1Surface Area of a Cube. SA = 6 * side^2, since a cube has 6 identical square faces.

2Surface Area of a Rectangular Prism (Box). SA = 2(lw + lh + wh), summing the areas of all 6 rectangular faces (in matching pairs).

3Surface Area of a Cylinder. SA = 2*pi*r^2 + 2*pi*r*h — the two circular ends plus the curved side, 'unrolled' into a rectangle.

4Surface Area of a Sphere. SA = 4*pi*r^2.

5Nets. A 2D 'unfolded' version of a 3D shape, useful for visualizing and calculating surface area by adding up each flat face.

Worked Examples

Find the surface area of a cube with side 4.

96 square units

Find the surface area of a rectangular prism with length 5, width 3, height 2.

62 square units

Find the surface area of a sphere with radius 3 (use pi ~ 3.14).

113.04 square units

Formulas

Cube: SA = 6*s^2

Rectangular prism: SA = 2(lw + lh + wh)

Cylinder: SA = 2*pi*r^2 + 2*pi*r*h

Sphere: SA = 4*pi*r^2

Practice Yourself

Find the surface area of a cube with side 5.

150

Find the surface area of a rectangular prism with l=4, w=3, h=2.

Find the surface area of a sphere with radius 2 (pi~3.14).

50.24