What the box holds
A carton is filled with grain, not wrapped in anything. How much grain does it hold?
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- Layer 1: 8 rows of 5, 40 unit cubes.
- Layer 2 stacks on top: 40 more.
- Layer 3 stacks on top: 40 more.
- 40 + 40 + 40 = 120 unit cubes.
The rule
A unit cube is a cube with edge 1 cm. Lay one flat layer of unit cubes on the carton floor. Stack a matching layer for each 1 cm of height.
Let l be the length, b the breadth and h the height.
volume of a cuboid = l × b × h
The carton is 8 cm by 5 cm by 3 cm. One layer holds 8 × 5 = 40 cubes. The height 3 cm makes 3 layers. Three layers hold 3 × 40 = 120, which is 8 × 5 × 3.
Volume counts the unit cubes that fill a solid. It is written in cubic units, such as cm³ (cubic centimetres). Surface area uses square units, such as cm² (square centimetres).
| Question | Working | Answer | Unit |
|---|---|---|---|
| How much covers it? | 2 × (40 + 24 + 15) | 158 | cm² |
| How much fills it? | 8 × 5 × 3 | 120 | cm³ |
A cube of edge 5 cm shows the difference. Its skin, the surface area, is 6 × 25 = 150 cm². Its filling, the volume, is 5 × 5 × 5 = 125 cm³.