Derived Units A unit obtained by combining or manipulating different SI units is called a derived unit Examples of derived units include volume and density

Measuring Volume Volume is the amount of space occupied by an object To measure the volume of a solid rectangle, you measure its length, width, and height and multiply the three numbers together (V = l x w x h). If measured in centimeters (cm), the volume would then be expressed in cubic centimeters (cm3)

Measuring Volume Another way to measure solid objects is by using the water displacement method This is the preferred way when the object does not have a mathematical equation for its volume or is an irregular shape. Volume = Final volume – Initial volume V = Vf – Vi

Measuring Liquid Volumes Liquid volumes indicate the capacity (or amount) that the container holds The most common units for liquid volumes are L and mL Liquid volumes are measured by graduated cylinders Sometimes liquid volumes such as doses of medicine are measured in cubic centimeters One cubic centimeter is exactly the same volume as one milliliter. 1 mL = 1 cm3 = 1cc

Density = Mass Volume D = M V or Density Combining the mass and volume of an object can be used to find the density of the object Density cannot be measured directly. It must be calculated from the objects mass and volume. Density is the mass per unit volume of a substance Density = Mass Volume D = M V or

M V D = Density You will need to know the equation for density We can use something called the Density Triangle to help us find other variables.

D V M V = M D M = D•V Density Density Triangle To use the Density Triangle, start by writing down the variable you want to find Cover up that variable with your hand Write down the remaining variables as you see them V = M D M = D•V

Density To get full credit on Density problems you must show four thing: The equation showing the variable you are trying to find Your work (Put the variables into the equation.) Your answer (What does your calculator show?) The Units (What are the appropriate units for the answer?)

D = = = 4.21 kg/L M V 17.6kg 4.18L Density Example 1 What is the density of a bowling ball if it has a mass of 17.6kg and a volume of 4.18L? D = = = 4.21 kg/L M V 17.6kg 4.18L

2150g M 2464cm3 D = = = 0.87 g/cm3 V Density Example 2 A textbook is 28cm x 4cm x 22cm and has a volume of 2464cm3. If the book has a mass of 2150g, what is the books density? D = = = 0.87 g/cm3 M V 2150g 2464cm3

M = D•V=(0.85g/mL)(114mL) = 96.9g Density Example 3 If a block of wood has a density of 0.85g/mL and is 114mL, what is the mass of the wood? M = D•V=(0.85g/mL)(114mL) = 96.9g Notice the mL cancelled out so the units for Mass are grams

V = = = 14.7 cm3 M D 39.8g 2.7g/cm3 Density Example 4 A piece of aluminum (39.8g) is used in a calculation. What is the volume of the aluminum? (The density of aluminum 2.7g/cm3) V = = = 14.7 cm3 M D 39.8g 2.7g/cm3