The relationship between units of volume and units of capacity We usually refer to the volume of a body and the capacity of a container. These refer to the same quantity. Therefore, we can relate units of volume and units of capacity. Imagine in a drinking glass the volume occupied by the glass material is 60 mL. This means that if we put it in a graduated container with water, the water level will rise by 60 mL. If the capacity of the drinking glass is 250 mL, we can pour up to 250 mL of liquid into it. If we pour in 100 mL, the volume of the liquid in the glass will be 100 mL, but the capacity of the glass will still be 250 mL. How many L are in 1 m3? How many L is 1 dm3 equal to? How many mL is 1 cm3 equal to? 1 m3 is a cube with side 1 m. Divide each m into 10 dm. Cut along all the lines. You will have 1 000 cubes of side 1 dm. 1 dm3 is a cube with side 1 dm. Divide each dm into 10 cm. Cut along all the lines. You will have 1 000 cubes of side 1 cm. 1 cm3 is a cube with side 1 cm. 1 cm3 is a thousandth of 1 dm3. Therefore, it is equal to 1 mL (millilitre). 1 m3 = 1 000 dm3 = 1 kL = 1 000 L 1 dm3 = 1 000 cm3 = 1 L 1 cm3 = 1 mL = 0.001 L 1 m3 1 dm3 1 cm 1 cm3 1 cm S O LV E D P R O B L E M 7 Write 0.5 daL in mL. 1. Identify the initial unit and the final unit. daL ® mL 2. To move from one to the other, go towards the end of the submultiples. The exponent of 10 will be positive. 3. Count the number of steps between the two units. This is the exponent of 10. daL L dL cL mL 4. Write it in the corresponding unit. 0.5 daL = 0.5 × 104 mL = 5 000 mL × 10 × 10 × 10 × 10 4 steps 26 Take a carton that states that it contains 1 L of milk or juice. a) Use a ruler to measure the length, width and height of the carton and then calculate the volume. b) Explain whether the carton can contain 1 L of liquid. 27 Convert these amounts: a) An Olympic-size swimming pool contains 2.5 million litres of water. Write this in m3. b) Soft drink cans have a volume of 33 cL. Write this in cm3. A C T I V I T I E S 1 100 mL 250 mL Capacity kL hL daL L dL cL mL : 10 : 10 : 10 : 10 : 10 : 10 × 10 × 10 × 10 × 10 × 10 × 10 19
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