📘 Lesson 12 of 16 · Geometry

📦 Surface Area

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.

Course progress: 75%

01 Key Concepts

Surface Area of a Cube

SA = 6 * side^2, since a cube has 6 identical square faces.

Surface Area of a Rectangular Prism (Box)

SA = 2(lw + lh + wh), summing the areas of all 6 rectangular faces (in matching pairs).

Surface 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.

Surface Area of a Sphere

SA = 4*pi*r^2.

Nets

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

02 Key Formulas

03 Solved Examples

Example 1 Find the surface area of a cube with side 4.
  1. Apply the formula: SA = 6*s^2 = 6*4^2 = 6*16.
Answer: 96 square units
Example 2 Find the surface area of a rectangular prism with length 5, width 3, height 2.
  1. Apply the formula: SA = 2(lw+lh+wh) = 2(5*3 + 5*2 + 3*2) = 2(15+10+6).
  2. = 2*31.
Answer: 62 square units
Example 3 Find the surface area of a sphere with radius 3 (use pi ~ 3.14).
  1. Apply the formula: SA = 4*pi*r^2 = 4*3.14*9.
  2. = 12.56*9.
Answer: 113.04 square units

04 Practice Questions

1Find the surface area of a cube with side 5.
150
2Find the surface area of a rectangular prism with l=4, w=3, h=2.
52
3Find the surface area of a sphere with radius 2 (pi~3.14).
50.24
4Find the surface area of a cube with side 10.
600
5What shape has surface area formula SA=4*pi*r^2?
A sphere

📄 Surface Area — Downloadable Worksheet

10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.