Previously, we reviewed the concept of volume as a measure of how much space a substance occupies. For example, imagine you have an object in the shape of a cube. From geometry, you remember that to calculate the volume of a cube, you simply need to measure the length of one side and then cube that value:

V_{cube} = side x side x side = side^{3}

A cube with a side of length 2.8 cm would have a volume of:

V_{cube} = 2.8 cm x 2.8 cm x 2.8 cm = 21.95 cm^{3}

If the cube has a mass of 59.27 g, we can use the mass and volume to calculate the density of the cube using the formula density = mass / volume (D=m/v). Inserting what we know into the equation: D = 59.27 g / 21.95 cm^{3} =2.7 g/cm^{3}

We know that density is an intensive property. It can help us identify what the block is made of (assuming the block is a pure substance).

- Question 9: What is the block made of? Hint: Click here to visit the list of the densities of common materials.

In the example above, we were tasked with calculating the volume of a cube. There are a number of familiar geometric forms, like rectangular prisms and spheres, that have formulas for volume that should be familiar to you (click here to review).

- Question 10: A student fills an empty balloon with helium gas. Conveniently, the helium-filled balloon is a perfect sphere! The student measures the radius of the balloon as 10.3 cm. Calculate the volume of the balloon.
- Question 11: Using the volume from Question 10 and the density of helium on the list of the densities of common materials, calculate the mass of helium gas in the balloon.

A graduated cylinder is used to most accurately measure the volume of a liquid. A graduated cylinder is also a really useful tool for measuring the volume of an irregularly shaped solid. We call that technique “water displacement” and the video below will explain how to do it:

Important things to note:

- Volume is unaffected by mass. Two objects can have the same volume but different masses.
- The relationship between mass and volume is density. Remember, density is equal to mass divided by volume.
- Volume can be measured in base units of liters or meters. In our example of the cube, volume was measured in cubic centimeters (cm
^{3}). In the water displacement method video, volume was measured in milliliters (mL). - When reading a graduated cylinder, bring your eye down to the level of the meniscus. The liquid in a graduated cylinder will form a U-shape. Read at the bottom of the U. Click here for more on how to read a graduated cylinder.

Question 12: A student wants to know if her gold-colored chain is solid gold or gold-plated (another metal covered in gold). After consulting the list of the densities of common materials, she knows the expected density of gold. Next, she measures the mass of her chain using an electronic balance and finds it to be 2.4 grams. What is the expected volume of the chain if it is really solid gold?

Question 13: What technique should the student use to determine the volume of her chain?

Question 14: Why does the overall size of a graduated cylinder affect how accurately we can measure volume?

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