Step by step
The question
Question: draw the net of a cube, side 3, and find its surface area.
cube, side 3
The surface area is the area of all the outside faces together.
A net shows every face flat.
surface area = all the faces added
1 Unfold it
We cut along some edges and fold it flat.
Matching faces have the same colour.
2 Area of each face
Top and bottom: 3 × 3 is 9.
= top and bottom: 3 × 3 = 9
Front and back: 3 × 3 is 9.
= front and back: 3 × 3 = 9
The two sides: 3 × 3 is 9.
= the two sides: 3 × 3 = 9
Careful!
Count every face in the net.
A box has 6 faces, not 3.
Careful: not 9 + 9 + 9 = 27 ✗
3 Add them all
We add all 6 faces: 54.
= SA = 9 + 9 + 9 + 9 + 9 + 9 = 54
4 Check
Let's check another way.
All 6 faces of a cube are the same square: 6 times 9 is 54.
So the answer is right!
6 × 3 × 3 = 6 × 9 = 54
Let's look back.
First: unfold it.
Then: area of each face.
Then: add them all.
Last: check.
Answer
= SA = 9 + 9 + 9 + 9 + 9 + 9 = 54