Measuring Volume

Core Idea

Volume is the amount of space an object takes up. For liquids, you measure volume using a graduated cylinder or measuring cup and read the measurement at the bottom of the curved surface (called the meniscus). For regular-shaped solids like a box, you can calculate volume by multiplying length times width times height. For oddly shaped solids like a rock, you can find the volume by dropping it into water and measuring how much the water level rises. Volume is measured in milliliters (mL), liters (L), or cubic centimeters (cm cubed).

How It's Best Learned

Have students measure liquid volumes using graduated cylinders, reading at the meniscus. Then give them irregular objects like rocks and marbles to measure by water displacement — record the water level before and after dropping the object in, and subtract to find the object's volume. Compare calculated volumes of rectangular blocks (L x W x H) with water displacement results.

Common Misconceptions

• Reading the graduated cylinder at the top of the meniscus instead of the bottom.
• Thinking volume and weight are the same thing (a heavy small object can have less volume than a light large object).
• Believing volume only applies to liquids.
• Confusing the water's volume with the object's volume when using water displacement.

Explainer

You have already learned about measuring liquid volume using milliliters and liters. Now it is time to expand that idea: volume is not just about liquids. Everything that takes up space has a volume — solids, liquids, and gases. Volume is simply the amount of space something occupies, and there are different ways to measure it depending on what you are measuring.

For liquids, you use a graduated cylinder or a measuring cup. Pour the liquid in and read the number at the bottom of the curved surface called the meniscus. Liquid in a narrow tube climbs up slightly at the edges, forming a curve. You always read at the lowest point of that curve, with your eyes level with the liquid. This gives you the volume in milliliters (mL) or liters (L).

For regular-shaped solids like boxes, bricks, or ice cubes, you can calculate the volume with math. Measure the length, width, and height, then multiply them together: length times width times height equals volume. A box that is 10 cm long, 5 cm wide, and 3 cm tall has a volume of 150 cubic centimeters (10 x 5 x 3 = 150 cm cubed). Cubic centimeters and milliliters are the same size, which is handy.

For irregularly shaped solids like rocks, keys, or toy figurines, math will not work because the shape is too complicated. Instead, you use a clever method called water displacement. Fill a graduated cylinder partway with water and record the level. Then gently drop the object in. The water level rises because the object takes up space that the water was occupying — the water gets pushed up and out of the way. The difference between the new water level and the old water level is the object's volume. If the water went from 50 mL to 68 mL, the object's volume is 18 mL.

This water displacement method was famously discovered by the ancient Greek scientist Archimedes, who realized that any object submerged in water displaces a volume of water exactly equal to its own volume. The story says he was so excited by this discovery that he jumped out of his bathtub and ran through the streets shouting "Eureka!" Whether or not that part is true, the method works perfectly and scientists still use it today.