Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 1, Part B:
Which Rock Is the Largest?

In This Part: Measuring Surface Area | Measuring Volume | Measuring Weight

 One method for determining the volume of irregular objects like rocks uses a technique called displacement. Archimedes (287-212 B.C.E.) is credited with discovering volume relationships. Here's how the story goes: Once there was a king who suspected that his crown might not be made of pure gold. He brought his problem to Archimedes, a "wise man" of the day. Archimedes pondered the question but didn't have an immediate solution. Later, as he was taking his bath, he noticed that the displacement of water in the tub was equal to the immersed part of his body. Archimedes leaped from the tub and ran naked through the streets, shouting, "Eureka!" His observation showed him how to solve the king's problem: Using the displacement-of-water method, he could easily calculate the volume of the crown. By comparing the weight of the crown to a lump of pure gold of the same volume, he found that the crown weighed less -- indeed it was not made of pure gold. As the king suspected, the crown was composed mostly of cheaper metals. Through measurement, Archimedes was able to expose the jeweler's dishonesty. Before you begin measuring, estimate the volume of the rock. (Later, you can compare your estimate with the approximate volume you've measured.) Take a graduated beaker marked in milliliters (or a measuring cup similarly marked) that is large enough to hold your rock. Fill the container halfway and record the water level. Note that to measure the volume by displacement, you will need to fully submerge the rock in the water. Displacement will be equal to the amount of space taken up by the rock.

 Problem B5 What units are you using to measure the water? Can you use this unit to measure the volume of a solid? Note 5

 One milliliter is 1/1,000 of a liter. There is an interesting relationship in the metric system that can be used to help you here -- namely, one milliliter is equivalent to 1 cm3. We often think of measuring solid objects using cubic centimeters, but because of this special relationship, we can also use milliliters (or liters). You have probably heard the medical term "cc's." When used this way, 200 cc's is equivalent to 200 cm3 or 200 mL. The medical term refers to units of length and volume, rather than units of liquid measure.    Close Tip One milliliter is one-thousandth of a liter. There is an interesting relationship in the metric system that can be used to help you here -- namely, one milliliter is equivalent to one cubic centimeter. We often think of measuring solid objects using cubic centimeters, but because of this special relationship, we can also use milliliters (or liters). You have probably heard the medical term "cc's." When used this way, "200 cc's" is equivalent to "200 cubic centimeters" or "200 milliliters." So, the medical term refers to units of length and volume, rather than units of liquid measure.

 Carefully place the rock in the water, and again note the height of the water. Determine the difference in water heights. Note 6

 Problem B6 If you found the volume of your rock using both displacement of water and displacement of rice, will the measurements be the same? Why or why not?

 Do you think that 1 mL of rice equals one cubic centimeter of rice?   Close Tip Do you think that one milliliter of rice equals 1 cm3 of rice?

 Session 1: Index | Notes | Solutions | Video