الأسبوع 26 · المجسّمات وقياس الحجم بالمكعبات · 3 دروس
2
Cubic units: measuring a third dimension
Discover Mathematics P5: Term 2, Unit 11, Lessons 1–3
GoalMeasure volume by counting unit cubes in layers, and write it in cubic units.
New words
unit cube · a cube with edges of 1 unit; its volume is 1 cubic unitcubic centimetre · the volume of a cube with edges of 1 cm, written 1 cm³layer · one flat level of unit cubes in a solid
Explanation
Area counts flat squares. Volume counts cubes, because a solid has a third dimension: height. A unit cube has edges of 1 cm, so its volume is 1 cubic centimetre (1 cm³). The volume of a solid is the number of unit cubes that fill it with no gaps and no overlaps. The easy way to count is by layers. A box 4 cm long and 3 cm wide has 4 × 3 = 12 cubes in the bottom layer. If the box is 2 cm high, there are 2 layers, so the volume is 12 × 2 = 24 cubes = 24 cm³. The answer is always written with the cubic unit. Never mix up 24 cm² (flat area) with 24 cm³ (space inside).
Worked examples
A box is 4 cm long, 3 cm wide and 2 cm high. One layer has 4 × 3 = 12 cubes. Two layers have 12 × 2 = 24 cubes. The volume is 24 cm³.
A box is 5 cm long, 2 cm wide and 3 cm high. One layer has 5 × 2 = 10 cubes, and there are 3 layers: 10 × 3 = 30 cubes. The volume is 30 cm³.
A row of 6 unit cubes has volume 6 cm³. Its flat shadow on the table covers 6 cm². Same number, but the first says how much space it takes up, and the second says how much surface it covers.
Class activity
Build with blocks. Use sugar cubes, dice or small building blocks as unit cubes. Build a box that is 3 cubes long, 2 wide and 2 high. Count the cubes layer by layer and write the volume. Build a different box with the same number of cubes and compare. How many different boxes can you make with exactly 12 cubes?
Practice
1
A prism is made of 3 layers with 8 unit cubes in each layer. What is its volume?
3 × 8 = 24 cubic units.
2
A box has a base of 6 cm by 2 cm and is 4 cm high. How many unit cubes fill it?
One layer: 6 × 2 = 12. Four layers: 12 × 4 = 48 cubes, so the volume is 48 cm³.
3
A cube is made of unit cubes, 3 along each edge. What is its volume?
One layer: 3 × 3 = 9. Three layers: 27. Volume 27 cm³.
4
Youssef says a box with volume 12 cm³ is the same as a square with area 12 cm². Is he right?
No. Cubic centimetres measure the space inside a solid. Square centimetres measure a flat surface.
5
Box A is 4 cm by 2 cm by 2 cm. Box B is 5 cm by 3 cm by 1 cm. Which has the greater volume, and by how much?
A: 4 × 2 × 2 = 16 cm³. B: 5 × 3 × 1 = 15 cm³. Box A is greater by 1 cm³.
