1. Derived Units

2. Learning Objectives I can explain what a derived unit is and list the derived units of the metric system. I can perform calculations involving volume and density.

3. Derived Units A unit that is defined by a combination of base units is called a derived unit. Examples of derived units: – Volume – Density

4. Volume Volume is the space occupied by an object.  V = l x w x h When each dimension is given in meters, the calculated volume has units of cubic meters (m 3 ) The derived SI unit for volume is the cubic meter.

5. Volume A liter (L) is equal to one cubic decimeter (dm 3 ).  1L = 1dm 3 For smaller quantities of liquid in the laboratory, volume is often measured in cubic centimeters (cm 3 ) or milliliters (mL). 1 mL = 1 cm 3

6. Volume The units milliliter and cubic centimeter are the same. mL is used for volumes of liquids and gases cm 3 is used for volumes of solids

7. Volume The volume of an irregularly shaped solid can be determined using the water displacement method. Determine initial and final volume. Subtract initial volume from final volume to get the volume of the object. – Example: 225 mL – 200 ml = 25mL Initial Volume Final Volume

8. Density Write both of these in your notes!

9. Calculating Density To use this triangle, cover up the unit you are solving for and use the equation that is left. For example, if you are solving for mass, you cover up mass which gives you m = D x V

10. Example Cover up volume and use the equation left over to solve for volume.

11. Example When a piece of aluminum is placed in a 25-mL graduated cylinder that contains 10.5 mL of water, the water level rises to 13.5 mL. The density of aluminum is 2.7 g/mL. What is the mass of the aluminum? We first have to solve for volume: 13.5 mL – 10.5 mL = 3.00mL M = D x V = 2.7 g/mL x 3.00 mL = 8.10 g Cover up mass and use the equation left over to solve for mass.

12. Density Equation Foldable Define volume Equation for volume Units of volume Define volume Equation for volume Units of volume Define mass Equation for mass Units of mass Define mass Equation for mass Units of mass Define density Equation for density Units of density (there are two) Define density Equation for density Units of density (there are two)

13. Finding Density Foldable Picture & ExampleExplanation Picture & Example Inside foldable

14. RoundTable Density 1.TM #1 starts off by writing down the needed and given units. 2.TM #2 writes the equation needed to solve the problem. 3.TM #3 performs the substitutions. 4.TM #4 performs the calculation recording the answer to the correct number of significant figures and with correct units. 5.TM #1 checks work before passing paper on to TM # 2 who starts the process over.