Question

The cup is a measure of volume widely used in cookbooks. One cup is equivalent to \(225 \mathrm{~mL}\). What is the density of clover honey (in grams per milliliter) if three quarters of a cup has a mass of \(252 \mathrm{~g}\) ?

Short answer

Answer: The density of clover honey is approximately 1.493 grams per milliliter (g/mL).

Step-by-step solution

Convert cup to milliliters (mL)

First, we need to convert three quarters of a cup to milliliters. We know that 1 cup is equivalent to 225 mL. Therefore, to find the volume of three-quarters of a cup, we need to calculate: $$ \frac{3}{4} \times 225 \mathrm{~mL} $$

Calculate the volume of three-quarters of a cup in milliliters (mL)

Now, let's calculate the volume of three-quarters of a cup in milliliters: $$ \frac{3}{4} \times 225 \mathrm{~mL} = 168.75 \mathrm{~mL} $$ So, the volume of three-quarters of a cup is 168.75 mL.

Divide mass by volume to find density

Now that we have both the mass and the volume of the honey, we can find the density by dividing the mass by the volume: $$ \text{Density} = \frac{\text{Mass}}{\text{Volume}} $$ Plugging in the values, we have: $$ \text{Density} = \frac{252 \mathrm{~g}}{168.75 \mathrm{~mL}} $$

Calculate the density of clover honey

Now let's calculate the density: $$ \text{Density} = \frac{252 \mathrm{~g}}{168.75 \mathrm{~mL}} = 1.493 \mathrm{~g/mL} $$ Therefore, the density of clover honey is approximately 1.493 grams per milliliter (g/mL).