Primary 6 Volume of cubes and cuboids
Volume tells us how much space a solid occupies. Multiply three perpendicular lengths, or multiply the area of one face by the distance to the opposite face.
Cube and cuboid
Compare the two solids row by row. Both have six faces and 12 edges. A cube has equal edges; a cuboid can have different length, breadth, and height.
| Compare | Cube | Cuboid |
|---|---|---|
| Shape | ||
| Faces | 6 equal square faces | 6 faces; opposite faces are equal |
| Edges | 12 equal edges | 12 edges; length, breadth, and height may differ |
| Volume | V = side × side × side | V = L × B × Hlength × breadth × height |
Find the volume of a cube
A cube has side length 4 cm. Find its volume.
- Choose the formula: V = side × side × side.
- Substitute: V = 4 × 4 × 4.
- Calculate: V = 64 cm³.
Answer: 64 cm³
Find the volume of a cuboid
A cuboid is 6 cm long, 4 cm in breadth, and 3 cm high. Find its volume.
- Choose the formula: V = L × B × H.
- Substitute: V = 6 × 4 × 3.
- Calculate: V = 72 cm³.
Answer: 72 cm³
Try together
Find the volume of a cube with edge length 5 cm.
Reveal the answer
5 × 5 × 5 = 125 cm³.
Finding a missing dimension
Start with V = L × B × H. Divide the volume by the product of the two known dimensions. Since base area = L × B, height can also be found by dividing volume by base area. Check that the answer has a length unit, such as cm.
Find the length
A cuboid has volume 240 cm³, breadth 4 cm, and height 5 cm. Find its length.
- Choose the formula: L = VB × H.
- Substitute: L = 2404 × 5.
- Calculate: L = 24020 = 12 cm.
Answer: 12 cm
Find the height
A cuboid has volume 240 cm³, length 10 cm, and breadth 4 cm. Find its height.
- Choose the formula: H = VL × B.
- Substitute: H = 24010 × 4.
- Calculate: H = 24040 = 6 cm.
Answer: 6 cm
Find the breadth
A cuboid has volume 180 cm³, length 9 cm, and height 4 cm. Find its breadth.
- Choose the formula: B = VL × H.
- Substitute: B = 1809 × 4.
- Calculate: B = 18036 = 5 cm.
Answer: 5 cm
Try together
A cuboid has volume 180 cm³, breadth 3 cm, and height 5 cm. Find its length.
Reveal the answer
L = 1803 × 5 = 12 cm.
Finding the area of a face
To find the area of the base face (L × B), divide the volume by the height. The diagram below shows that the height is perpendicular to the base.
Find the highlighted base area
A cuboid has volume 180 cm³ and height 5 cm. Find the area of its base.
- Choose the formula: V = base area × height.
- Rearrange: base area = Vheight.
- Calculate: base area = 1805 = 36 cm².
Answer: 36 cm²
Try together
A cuboid has volume 96 cm³ and height 4 cm. Find the area of its base.
Reveal the answer
Base area = 964 = 24 cm².
Using square and cube roots
A square root undoes squaring; a cube root undoes cubing. Here, use perfect squares and perfect cubes you can check by multiplication.
Find the side of a square face
The face found above has area 36 cm². If that face is a square, find one side.
- Write the square: s² = 36.
- Use the square root: s = .
- Check: s = 6 cm because 6 × 6 = 36.
Answer: 6 cm
Find the edge of a cube
A cube has volume 216 cm³. Find its edge length.
- Write the cube: s³ = 216.
- Use the cube root: s = .
- Check: s = 6 cm because 6 × 6 × 6 = 216.
Answer: 6 cm
Try together
A cube has volume 125 cm³. Find its edge length.
Reveal the answer
= 5 cm, because 5 × 5 × 5 = 125.