Unit Conversion (density): A storage tank located at a food processing facility has a total volume of 634 ft3.  The entire volume of the tank is occupied by a liquid slurry with a known mass of 1,502 slugs.  Based on this information, estimate the density of the slurry in kg/m3. Report your answer to one decimal place.

To estimate the density of the slurry in \( \text{kg/m}^3 \), we need to convert the given volume from cubic feet (\( \text{ft}^3 \)) to cubic meters (\( \text{m}^3 \)) and the mass from slugs to kilograms (kg). After converting the units, we can calculate the density using the formula:

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

### Step 1: Convert Volume from Cubic Feet to Cubic Meters

1 cubic foot is equal to 0.0283168 cubic meters. Thus, we convert 634 cubic feet to cubic meters:

\[
634 \, \text{ft}^3 \times 0.0283168 \, \text{m}^3/\text{ft}^3 = 17.9509 \, \text{m}^3
\]

### Step 2: Convert Mass from Slugs to Kilograms

1 slug is equal to 14.5939 kilograms. Thus, we convert 1,502 slugs to kilograms:

\[
1502 \, \text{slugs} \times 14.5939 \, \text{kg/slug} = 21,918.6778 \, \text{kg}
\]

### Step 3: Calculate the Density in \( \text{kg/m}^3 \)

Now, we use the converted values to find the density:

\[
\text{Density} = \frac{21,918.6778 \, \text{kg}}{17.9509 \, \text{m}^3} = 1,221.1 \, \text{kg/m}^3
\]

### Conclusion

The density of the slurry is approximately **1,221.1 kg/m³**.

If you have any questions or want more details on this solution, feel free to ask!

### Related Questions:

1. How do you convert slugs to pounds and pounds to kilograms?
2. What is the relationship between mass, volume, and density?
3. How does the density of a substance affect its buoyancy?
4. What are the differences between the metric system and the imperial system for volume and mass?
5. How can the density of a slurry affect its flow properties in a pipeline?

**Tip:** Remember that density is a key property in many fields, including engineering, physics, and chemistry, as it affects how substances interact with each other.

A storage tank located at a food processing facility has a total volume of 634 ft³. The entire volume of the tank is occupied by a liquid slurry with a known mass of 1,502 slugs. Based on this information, estimate the density of the slurry in kg/m³. Report your answer to one decimal place.

Learn how to estimate the density of a liquid slurry in kg/m³ by converting volume from cubic feet to cubic meters and mass from slugs to kilograms. This problem covers key concepts in unit conversion and density calculation, suitable for students in Grades 9-12.

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