Millilitres, cubic centimetres and displacement · Usually met around P6
Capacity and volume
1 mL = 1 cm³, 1 L = 1000 mL.
How to do it
Method
1 mL = 1 cm³, 1 L = 1000 mL
20 × 10 × 15 = 3000 mL, so 3 L
One more example
A 600 cm³ stone: 600 ÷ 200 = 3 cm
In full
A space of 1 cm³ holds exactly 1 mL of water. So 1 mL = 1 cm³, and 1 L = 1000 mL = 1000 cm³. A container's capacity = its inside length × width × height. The water's volume = length × width × the water's depth (not the tank's height). A tank that is 20 cm × 10 cm × 15 cm inside: 20 × 10 = 200, 200 × 15 = 3000, so it holds 3000 mL, and 3000 ÷ 1000 = 3, so 3 L. When a stone sinks in water, the water rises, and the extra water has the same volume as the stone. A base of 20 cm × 10 cm and a rise of 3 cm → 200 × 3 = 600, so the stone is 600 cm³. Going backwards, a volume ÷ the base's area gives a height. A 600 cm³ stone: 600 ÷ 200 = 3, so the water rises 3 cm. Pour in 3 L: 3 × 1000 = 3000, 3000 ÷ 200 = 15, so the water is 15 cm deep.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Volume of the stone = ? cm³
Show the answer and working
Answer: Volume of the stone = 80 cm³
The water that rose takes up the stone's volume: 10 × 8 = 80, 80 × 1 = 80, so 80 cm³
Example 2
The water rises by ? cm
Show the answer and working
Answer: The water rises by 4 cm
The water that rose has the stone's volume; divide by the base: 10 × 8 = 80, 320 ÷ 80 = 4, so it rises 4 cm
Example 3
The water is ? cm deep
Show the answer and working
Answer: The water is 2 cm deep
Depth = the water's volume ÷ the base's area, and 1 mL = 1 cm³: 20 × 20 = 400, 800 ÷ 400 = 2, so 2 cm
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