Calculating volume and area: cubed and squared metric conversions

What units do we use to record volume?

Volume Volume is the quantity of space that something occupies There are several SI units used to measure volume: cubic meter (m3) cubic centimeter (cm3) litre (L) millilitre (mL) For volume, why are our meter units cubed?

For the volume of a solid cube, we multiply the length of each side (length · width · height) 6 cm · 4 cm · 7 cm = 168 cm3

Calculating volume: regular shaped solids The volume of an object is calculated by multiplying the length (l) times the width (w) times the thickness (t). volume = l × w × t All three measurements must be in the same units. For example: If an object measures 3 cm by 2 cm by 1 cm, the volume is 6 cm3 (cm3 is cubic centimeters)

Volumes of liquids and gases The litre(L) is the basic unit of volume in the metric system. One litre is defined as the volume occupied by a cube that is 10 cm on each side

We use litre units when we are measuring the volume of a liquid We use litre units when we are measuring the volume of a liquid. Typically, a graduated cylinder is used for this type of measurement Conversion factors between volume units; 1 m3 = 1,000 L 1 cm3 = 1 mL 1 mL = 0.001 L 1 L = 1 dm3 = 0.001 m3

Calculating volume: irregular shaped solids and gases: displacement If a solid has an irregular shape, its volume cannot be determined by measuring its dimensions. You can determine its volume indirectly by measuring the amount of water it displaces. This technique is called volume by displacement. Volume by displacement can also be used to determine the volume of a gas. Let’s try some practice…

We can calculate volume of solid objects by displacement…. If you want to measure the volume of an irregularly shaped piece of jade: partially fill a volumetric flask with water and measure the volume of the water. add the jade, and measure the difference in volume. The volume of the jade is 10.5 mL.

We can also measure gas volume using the displacement method… You want to measure the volume of gas given off in a chemical reaction. The gas produced displaces the water in the flask into the beaker. The volume of water displaced is equal to the volume of gas produced

Metric volume conversions (m3 to cm3…) m3 to cm3 and vice versa… Remember that you are calculating volume NOT distance Conversion factors needed: 1 m = 100 cm = 1 X 102 cm So 1 m3 = (1 X 102)3 1 m3= 100 cm X 100 cm x 100 cm = 1 X 106 cm3

Metric volume conversions (m3 to L…) m3 to litres and vice versa… Remember that you are calculating volume NOT distance Conversion factors needed: 1 cm3 = 1 ml 100 cm = 1 m 1000 ml = 1 L 1 m3 = 1000 L or 1 X 106 cm3

Metric squared units conversions (just as easy) Visualise your area as a square and make sure you use the correct units needed for the conversion E.g. convert 1 km2 into μm2 1 km2 = 1 km X 1 km 1 m = 106 μm Then 1 km = 1 X 103 X 106 μm So 1 km2 = (1 X 103 X 106)2 μm2 = 1 X 1018 μm2

Let’s try some practice problems…