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Surface area of a cube: six equal faces
Discover Mathematics P6: Term 2, Unit 13, Lessons 1–2
GoalFind the surface area of a cube as 6 equal faces and solve problems about cubes.
New words
cube · a solid with six equal square facesedge · the line where two faces meet; a cube has 12 equal edgessquare number · a number multiplied by itself, such as 4 × 4 = 16
Explanation
A cube is a cuboid whose length, width and height are all equal to the edge a. Every face is a square of area a × a. A cube has 6 faces, so the surface area is 6 × a × a. For an edge of 4 cm, one face is 4 × 4 = 16 cm² and the surface area is 6 × 16 = 96 cm². To go backwards, divide the surface area by 6 to get one face, then find which number multiplied by itself gives that face. A cube with surface area 150 cm² has faces of 150 ÷ 6 = 25 cm², so the edge is 5 cm.
ƒFormula
Surface area of a cube = 6 × a × a
a is the length of one edge.
Worked examples
A cube has edge 4 cm. One face: 4 × 4 = 16 cm². Six faces: 6 × 16 = 96 cm².
A cube has edge 10 cm. One face is 100 cm², so the surface area is 600 cm².
The surface area of a cube is 150 cm². One face: 150 ÷ 6 = 25 cm². Since 5 × 5 = 25, the edge is 5 cm.
Class activity
Wrap a cube. Take a small cube-shaped box. Measure its edge and find how much wrapping paper you need, without overlaps. Check by tracing the faces on paper.
Practice
1
Find the surface area of a cube with edge 6 cm.
6 × 6 = 36, and 6 × 36 = 216 cm².
2
Find the surface area of a cube with edge 8 cm.
8 × 8 = 64, and 6 × 64 = 384 cm².
3
A cube has surface area 54 cm². Find its edge.
54 ÷ 6 = 9, and 3 × 3 = 9, so the edge is 3 cm.
4
A gift box is a cube with edge 20 cm. How many cm² of paper cover it?
One face 400 cm². 6 × 400 = 2,400 cm².
5
Hana says a cube with edge 5 cm has surface area 5 × 5 = 25 cm². What did she forget?
25 cm² is only one face. A cube has six: 6 × 25 = 150 cm².