Surface Area and Volume • Topic 1 of 7

Cubes

A cube has six identical square faces and all edges equal. Its volume is edge³ (the edge cubed), and its total surface area is 6 × edge², since there are six square faces each of area edge². For an edge of 4, the volume is 64 and the surface area is 6 × 16 = 96. Both measures depend on a single length, so one edge determines everything, and you can reverse either: the edge is the cube root of the volume or the square root of (surface area ÷ 6). Keep volume (cubic units) distinct from surface area (square units) — that is the usual SAT trap.

An oblique cube with equal edgesCubesVolume = s³    Surface area = 6s²

✅ Solved examples

1. A cube has edge 4. Find its volume.
4³ = 64.
2. A cube has edge 4. Find its surface area.
6 × 4² = 6 × 16 = 96.
3. A cube has edge 3. Find its volume.
3³ = 27.
4. A cube has edge 5. Find its surface area.
6 × 25 = 150.

✏️ Practice — try these, take hints as needed

1. A cube has edge 2. Find its volume.
edge³.
2³.
—
8.
2. A cube has edge 3. Find its surface area.
6 × edge².
6 × 9.
—
54.
3. A cube has edge 6. Find its volume.
6³.
—
—
216.
4. A cube has edge 10. Find its surface area.
6 × 100.
—
—
600.
5. A cube has edge 5. Find its volume.
5³.
—
—
125.

📝 Topic test — 8 questions

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