Practice comparing real-world ratios.

Question

A 3-column table with 4 rows. Column 1 is labeled Liquid with entries water, glycerin, milk, olive oil. Column 2 is labeled Mass (grams) with entries 1, 1.26, 1.03, 0.98. Column 3 is labeled Volume (centimeters per gram cubed) with entries 1, 1, 1, 1.

Density is the ratio of mass to volume.
Density = StartFraction mass Over volume EndFraction
Compare the density of different liquids with the same volume.

The liquid with the greatest density is
.
The liquid with the least density is
.

Answer 1

To find the density of each liquid, we will use the formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

From the table, we see that the volume for all liquids is the same (1 cm³). Therefore, the density is essentially equal to the mass of the liquids, which we have as follows:

1. Water:

   • Mass = 1 g
   • Density = \( \frac{1 \text{ g}}{1 \text{ cm}^3} = 1 \text{ g/cm}^3 \)

2. Glycerin:

   • Mass = 1.26 g
   • Density = \( \frac{1.26 \text{ g}}{1 \text{ cm}^3} = 1.26 \text{ g/cm}^3 \)

3. Milk:

   • Mass = 1.03 g
   • Density = \( \frac{1.03 \text{ g}}{1 \text{ cm}^3} = 1.03 \text{ g/cm}^3 \)

4. Olive Oil:

   • Mass = 0.98 g
   • Density = \( \frac{0.98 \text{ g}}{1 \text{ cm}^3} = 0.98 \text{ g/cm}^3 \)

Now we can compare the densities of the different liquids:

• The liquid with the greatest density is glycerin (1.26 g/cm³).
• The liquid with the least density is olive oil (0.98 g/cm³).