Answered

A crate of medicine with a density of 167 pounds per cubic foot will be shipped from the U.S. to England. What is the crate's density in kilograms per cubic meter?

First, fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side of the equation.

Ratios:
[tex]\[
\frac{1 \, m^3}{35.3 \, ft^3}
\][/tex]
[tex]\[
\frac{35.3 \, ft^3}{1 \, m^3}
\][/tex]
[tex]\[
\frac{1 \, kg}{2.2 \, lb}
\][/tex]
[tex]\[
\frac{2.2 \, lb}{1 \, kg}
\][/tex]

[tex]\[
167 \, \frac{lb}{ft^3} \times \square \times \square = \square \frac{kg}{m^3}
\][/tex]



Answer :

GinnyAnswer
To convert the density from pounds per cubic foot (lb/ft³) to kilograms per cubic meter (kg/m³), you need to use two conversion ratios: one for mass and one for volume. The relevant ratios are:

- [tex]\(\frac{1 \text{ kg}}{2.2 \text{ lb}}\)[/tex]
- [tex]\(\frac{1 \text{ m}^3}{35.3 \text{ ft}^3}\)[/tex]

Given that the density is 167 lb/ft³, let's place these in the equation to get the density in kg/m³:

[tex]\[ 167 \frac{\text{lb}}{\text{ft}^3} \times \frac{1 \text{ kg}}{2.2 \text{ lb}} \times \frac{1 \text{m}^3}{35.3 \text{ft}^3} = ? \frac{\text{kg}}{\text{m}^3} \][/tex]

To solve this:

1. Multiply 167 by [tex]\(\frac{1 \text{ kg}}{2.2 \text{ lb}}\)[/tex]:

[tex]\[ 167 \times \frac{1 \text{ kg}}{2.2 \text{ lb}} = 75.9090909090909 \frac{\text{kg}}{\text{ft}^3} \][/tex]

2. Now, take the result and multiply by [tex]\(\frac{1 \text{ m}^3}{35.3 \text{ ft}^3}\)[/tex]:

[tex]\[ 75.9090909090909 \times \frac{1 \text{ m}^3}{35.3 \text{ ft}^3} = 2.15039917589493 \frac{\text{kg}}{\text{m}^3} \][/tex]

Thus, the crate's density in kilograms per cubic meter is:

[tex]\[ 2.15039917589493 \frac{\text{kg}}{\text{m}^3} \][/tex]

Rounded to the nearest hundredth, the density is:

[tex]\[ 2.15 \frac{\text{kg}}{\text{m}^3} \][/tex]

Therefore, the final answer, rounded to the nearest hundredth, is:

[tex]\[ 2.15 \frac{\text{kg}}{\text{m}^3} \][/tex]

Other Questions