1. Volume and Mass
CPS
Chapter 1

2. Introduction If I had a stack of gold coins, how would I count them?
What if I had several stacks of gold coins….would I count them all? What could I do differently?
I might make a scale instead….then if I wanted to know the amount of gold in the coins, I could just count the coins.

3. Introduction…
If I wanted to find out how much gold was in a bar of gold, there are several things that I could do. How do you think we could measure the gold?
What if we took tiny cubes, all the same size, and used them to fill a space the same size of the cube? We could count the cubes and know how much gold there was.

4. 1.2 Volume
An even easier solution would be to count only the cubes along each edge and multiply them
(#cubes in height)
(#cubes in width) (#cubes in depth)
Height*width*depth

5. Units of Measurement Meter = standard unit of measurement
Centimeter = .01 meters (1/100 of a meter)
When we multiply the height x width x depth (length), we cube the centimeter, so the units become cubic centimeter, or cm3
When measuring liquids, we use the unit milliliter. A mL is 1/1000 of a liter (.001 L)

6. Comparing Volumes
We use volume to compare different amounts of the same substance.
For a solid we can multiply the three sides of a rectangular solid
For a liquid, we can use a graduated cylinder. Graduated cylinders have unit measurements along the side, and because liquids take the place of their container, we can easily measure the amount.

7. Volumes of Irregular Shapes
We don’t need to use extensive geometry to find the volume of an irregularly-shaped object. We can use a method called “water displacement.”
Place some water into a graduated cylinder and measure the amount. (Call it V1)
Put the object in the graduated cylinder.
Measure the new volume. (Call it V2)
Subtract (V2-V1). What you have left is the volume of the object.

8. 1.3 Reading Scales
The smallest divisions on a ruler are 0.1 cm, or 1 mm apart.
When you measure something, very rarely is it exactly on a line. Usually it falls between two lines. If you look at the paperclip above, the length falls between 4.7 and 4.8 cm. We estimate the last number of the measurement since we do not know exactly what it is. Since it is closer to 4.7, we would probably say that it is 4.72 cm.

9. More on Reading Scales
If it fell exactly on the line, we would report the reading as 4.70 cm. That gives us a better idea of exactly how long the paperclip is.

10. 1.5 Shortcomings of Volume
When a solid dissolves in a liquid, sometimes the volume changes (decreases)
Gas is easily compressed (lots of gas can be shoved into the same space-like pumping a bike tire)
Difficulty in comparing differences between a solid and a liquid, or a liquid and a gas.

11. 1.6 Mass
Mass has been used as a measurement tool for thousands of years…
Equal arm balances were used early on-people quickly realized they responded to MASS. The type of mass did not matter
A standard mass is necessary in order to compare different types of objects
Grams are the standard unit for mass
1 kilogram = 1000 grams (1 kg=1000g)

12. More Interesting Units of Measurement
1 ml = 1cm3
1 kg = 2.2 lb

13. 1.10 Electronic Balances Pan moves slightly when object put on it
The tare button puts the number (mass) on the screen back to zero.
Be careful to make sure the units listed along the edge of the screen are the ones that you are measuring. Ask your teacher for assistance with this feature.