Step by step
The question
Question: find the surface area of a cube with sides 3 cm.
1 Count the faces
The surface area is the area of all the outside faces.
A box has 6 faces.
They come in 3 pairs, the same size.
2 Top and bottom
The top is 3 by 3.
Its area is 3 times 3, that is 9.
The bottom is the same.
Two faces of 9: 2 times 9 is 18.
2 × (3 × 3) = 2 × 9 = 18 cm2
3 Front and back
The front is 3 by 3.
Its area is 3 times 3, that is 9.
The face behind it is the same.
Two faces of 9: 2 times 9 is 18.
2 × (3 × 3) = 2 × 9 = 18 cm2
4 The two sides
The side is 3 by 3.
Its area is 3 times 3, that is 9.
The face behind it is the same.
Two faces of 9: 2 times 9 is 18.
2 × (3 × 3) = 2 × 9 = 18 cm2
5 Add all the faces
Add the three pairs: 18 + 18 + 18.
S = 18 + 18 + 18
18 plus 18 is 36.
S = 36 + 18
36 plus 18 is 54.
So the surface area is 54 cm².
S = 54 cm2
Let's look back.
First: count the faces.
Then: top and bottom.
Then: front and back.
Then: the two sides.
Last: add all the faces.
Answer
S = 54 cm2