**Introduction**

Every object takes up space. The amount of space an object occupies is known as volume. For objects of a simple geometric shape (e.g. spheres, cubes, etc.), the volume can be calculated with a formula. For example, the formula for the volume of a sphere is (4/3)*pi*radius^3. However, in real experiments and daily life, objects are rarely of a simple geometric shape, and there is no easy formula to determine the volume.Therefore, a better approach than dimensional analysis is needed.

We will use water displacement to calculate the volume of small, irregularly-shaped household objects. Consider a bathtub filled with water. When you get in the bathtub, you displace a volume of water equal to the volume of your body that is submerged. This is because you are now occupying the space that the water previously occupied. This principle is called Archimedes' Principle. Using this concept, the volume of any object can be calculated.

We will use this principle to calculate the volume of a household item that can fit in a measuring cup.

**Materials**

To calculate the volume of a small, household item you will need five things:

1. A measuring cup with clearly marked intervals defining volume in milliliters

2. A dark marker

3. Notebook paper

4. Pencil/Pen

5. An object that will fit in the measuring cup (we will calculate the volume of this object)*

**Some very small objects (e.g. paperclips, needles, etc.) will not displace enough water to make a good measurement (see the last step "Further Investigations" for more information).*

**Cost**

The total cost of all these items is less than $10, not including the object to be measured.

**Time**

The experiment should not take more then ten minutes. It is quick and easy!

**NOTE:**

**For the sake of your object, make sure it is waterproof.**

## Step 1: Check That the Object Fits in the Measuring Cup

To calculate the volume of an object it must be able to fit in the measuring cup and be **completely submerged** if the measuring cup was filled with water.

## Step 2: Place the Object in the Cup

## Step 3: Fill the Cup With Just Enough Water to Completely Cover the Object

Note: The amount of water used here is independent of the volume of the object. Just be sure the final water level in the measuring cup does not exceed the dimensions of the measuring cup.

## Step 4: Make a Measurement

Draw a line on the outside of the measuring cup with the dark marker at the height of the water in the cup. The line should be drawn on the** milliliter side **of the measuring cup.

## Step 5: Remove the Object and Make Another Measurement

Remove the object and draw another dark line on the measuring cup at the height of the new water line. Make sure this line **is below the first line on the milliliter side **of the measuring cup. Pour the water down the sink when done; it will make the lines easier to see.

## Step 6: Record the Volume at Each Line

Now, get the paper and pencil or pen. Record the volume at the top dark line. Make sure the volume you are recording is in milliliters. If the dark line isn't at a clear line on the measuring cup, estimate the value to the best of your ability. Then, repeat for the bottom line.

## Step 7: Subtract the Lower Number From the Higher Number to Find the Volume

Now that you have two values for the volume in milliliters, **subtract the lower number from the higher number. **This difference is the volume of the object in milliliters.

To convert to a more useful quantity, note that **1 milliliter = 1 cubic centimeter**. You now know the volume of your object in cubic centimeters!

## Step 8: Further Investigations Using a Graduated Cylinder

For a more precise measurement of volume, perform the same process using a graduated cylinder instead of a measuring cup. This will produce more accurate measurements because the graduated cylinder has a higher precision of measurement.

*For very small objects this is the only way to accurately measure their volume using Archimedes' method because graduated cylinders have the precision necessary to measure the tiny water displacement these objects cause.