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
- 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
03 Solved Examples
Example 1 Find the surface area of a cube with side 4.
- 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.
- Apply the formula: SA = 2(lw+lh+wh) = 2(5*3 + 5*2 + 3*2) = 2(15+10+6).
- = 2*31.
Answer: 62 square units
Example 3 Find the surface area of a sphere with radius 3 (use pi ~ 3.14).
- Apply the formula: SA = 4*pi*r^2 = 4*3.14*9.
- = 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.