#### Measuring Irregular Volumes

You have learned how to measure the volume of liquids in various graduated containers such as the graduated cylinder. You also learned to calculate the volume of regular solid shapes, such as cubes, rectangular prisms, spheres, and cylinders using mathematical formulas and simple length and circumference measurements. But how do you determine the volume of irregularly-shaped solid objects? For example, how could you determine the volume of a rock like the one shown to the right?

Imagine you have a glass filled to the very top with water. It could not hold even a single drop more. Now imagine that you insert a rock into the filled glass. What happens?

As you might have guessed, the water overflows onto the table. But did you also guess that the amount of water that overflows is *exactly* the same as the volume of the rock? This is the principle that you will use to perform volume displacement measurements.

#### LabLearner Tabs: Using the Volume Displacement Method

Learn more about the volume displacement method of determining the volume of irregularly-shaped solid objects by clicking on the tabs below. Start with Tab One: Using the Volume Displacement Method. Then move on to the next tab Tab Two: Example Volume Displacement Readings in order to see more volume displacement examples.

- Volume Displacement
- Tab One: Using the Volume Displacement Method
- Tab Two: Example Volume Displacement Readings

## Archimedes

Archimedes was a scientist who lived in Greece around 300BC. A story goes that he had a problem of trying to determine the volume of an irregularly-shaped solid object (the King’s crown). One day, his bath was filled too full – right to the very brim. When Archimedes got into the tub, water overflowed and he immediately realized that the water that overflowed was equal to his body’s volume. He discovered volume displacement!

It is also told that upon making this discovery, he was so excited he shouted aloud “*Eureka, Eureka!*“. Since that time, many people, not just scientists, will say the word “*Eureka*” when they figure something out.

## Using the Volume Displacement Method

1. The volume displacement method is used when measuring the volume of aa solid object that is irregularly shaped *and* sinks in water.

**Determine whether the volume displacement method can be used**:

2. Fill a beaker halfway with water. Be sure that the beaker is large enough that the object or substance has plenty of room. If not, choose a larger container.

3. Add the object or substance to the beaker.

4. If the object floats, only the part of the object’s volume that is underwater is displaced. This will not give you an accurate measurement of the object’s total volume, so the volume displacement method cannot be used.

**Using the volume displacement method to determine the volume of an object:**

5. Any calibrated volumetric piece of equipment such as a 50 ml, 100 ml, 250 ml, 500 ml or 1000 ml graduated cylinder can be used. A 100 ml or 250 ml graduated cylinder often works best. Basically, the smallest volume graduated cylinder in which your sample can fit will give the most accurate result.

6. Observe the size of the object to determine which piece of volumetric equipment can be used. The object should fit into it and be easily removed.

7. Pour enough water into your selected volumetric container, for example a graduated cylinder, so that when the object is added it will be totally under the water but not cause the water level to spill over or go above the graduation markings. Record the volume of water in milliliters (ml). This is your starting volume of water.

8. Tilt the graduated cylinder and place the object in the cylinder. Tilting the graduated cylinder helps prevent water from splashing out of the cylinder or up its inner sides. Observe and record the total volume contained in the graduated cylinder in milliliters (ml). This is the volume of water plus the sample.

9. Determine the volume of the object alone. Subtract the volume of water recorded when the graduated cylinder contained water alone from the volume when the graduated cylinder contained water and the sample. For example:

** 72 ml Volume of water + sample**

** -50 ml Starting volume of water alone**

** 22 ml Volume of sample**

10. Next, convert the volume in units of milliliters (ml) to the volume in units of cubic centimeters (cm^{3}). One ml of water is equal to one cm^{3}.

**1 ml = 1 cm ^{3}**

Therefore, the volume of the object is:

**22 ml = 22 cm ^{3}**

## Example Volume Displacement Readings

Determine the volume of the sample placed in each of the graduated containers below.

**Using a 500 ml Graduated Cylinder (notice that each mark is 5 ml):**

**Sample 1: 450 ml – 415 ml = 35 ml (35 cm ^{3})**

**Sample 2: 275 ml – 345 ml = 70 ml (70 cm ^{3})**

**Using a 100 ml Graduated Cylinder (notice that each mark is 1 ml):**

**Sample 3: 60 ml – 43 ml = 17 ml (17 cm ^{3})**

**Sample 4: 57 ml – 52 ml = 5 ml (5 cm ^{3})**

**Using a 15 ml Centrifuge Tube (notice that each mark is 0.5 ml):**

**Sample 5: 5.5 ml – 5.0 ml = 0.5 ml (0.5 cm ^{3})**