Stage 11 · Shape & space
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: 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 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. A stone sunk in water makes it rise, and the water that rose has the stone's volume: a base of 20 cm × 10 cm and a rise of 3 cm → 200 × 3 = 600, so the stone is 600 cm³. Backwards, a volume divided by the base's area is a height: a 600 cm³ stone, 600 ÷ 200 = 3, so the water rises 3 cm; 3 L poured in, 3 × 1000 = 3000, 3000 ÷ 200 = 15, so it stands 15 cm deep.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
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 2
Volume of the stone = ? cm³
Show the answer and working
Answer: Volume of the stone = 1500 cm³
The water that rose takes up the stone's volume: 30 × 10 = 300, 300 × 5 = 1500, so 1500 cm³
Example 3
Capacity of the tank = ? mL
Show the answer and working
Answer: Capacity of the tank = 896 mL
Capacity = inside length × width × height: 14 × 8 = 112, 112 × 8 = 896, and 896 cm³ = 896 mL, so 896 mL
Example 4
Water in the tank: ? L
Show the answer and working
Answer: Water in the tank: 1 L
The water's volume = length × width × its depth (not the tank's height): 10 × 10 = 100, 100 × 10 = 1000, so 1000 mL; 1 L = 1000 mL: 1000 ÷ 1000 = 1, so 1 L
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