Week 27 · Same volume, different shape; the volume formula · 3 lessons
3
Using the formula for volume
Discover Mathematics P5: Term 2, Unit 11, Lessons 4–6
GoalUse the formula to solve volume problems in cm³ and m³, and to find a missing dimension.
New words
cubic metre · the volume of a cube with edges of 1 m, written 1 m³missing dimension · a length, width or height you must findlitre · a unit of capacity; 1 litre = 1,000 cm³
Explanation
To solve a volume problem, write the formula, put in the numbers with their units, and multiply. Use cm³ for small things and m³ for large things such as a room or a swimming pool. To find a missing dimension, divide: if V and the base area are known, h = V ÷ B; if V, l and w are known, h = V ÷ (l × w). Capacity and volume are linked: a container whose volume inside is 1,000 cm³ holds 1 litre. So a tank of 40 cm by 25 cm by 20 cm has V = 40 × 25 × 20 = 20,000 cm³ and holds 20 litres of water. Always check your answer: multiply the three dimensions back to see that you get the volume.
Unit
Edge of unit cube
Used for
cubic centimetre
1 cm
a small box, a block
cubic metre
1 m
a room, a pool, a truck
Worked examples
A fish tank is 50 cm long, 30 cm wide and 40 cm high. V = 50 × 30 × 40 = 1,500 × 40 = 60,000 cm³. Since 1,000 cm³ is 1 litre, the tank holds 60 litres.
A storage room is 4 m long, 3 m wide and 3 m high. V = 4 × 3 × 3 = 36 m³. We use cubic metres because the room is large.
A box has volume 360 cm³ and a base of 12 cm by 5 cm. The base area is 12 × 5 = 60 cm². The height is 360 ÷ 60 = 6 cm. Check: 12 × 5 × 6 = 360.
Class activity
Volume of a classroom. Measure the length, width and height of your room in metres (round to whole metres). Calculate its volume in cubic metres. Then estimate how many children, each taking about 1 cubic metre, could stand inside. Compare with a friend’s room.
Practice
1
A tea box is 12 cm long, 8 cm wide and 5 cm high. Find its volume.
12 × 8 = 96 and 96 × 5 = 480 cm³.
2
A pool is 10 m long, 5 m wide and 2 m deep. How many cubic metres of water fill it?
10 × 5 × 2 = 100 m³.
3
A tank is 50 cm by 20 cm by 30 cm. What is its volume, and how many litres does it hold?
50 × 20 × 30 = 30,000 cm³ = 30 litres.
4
A box has volume 150 cm³ and a base of 10 cm by 5 cm. How high is it?
Base area 10 × 5 = 50. Height 150 ÷ 50 = 3 cm.
5
A cube-shaped tin has edges of 10 cm. Find its volume and say how many litres it holds.
