Question

the density of a certain material is such that it weighs 810 grams per cubic foot of volume. express this density in milligrams per liter. round your answer to the nearest whole number.
*note: you must use these exact conversion factors to get this question right.
weight / mass volume
1 pound (lb) = 16 ounces (oz) 1 cup (cup) = 8 fluid ounces (fl oz)
1 ton (ton) = 2000 pounds (lb) 1 pint (pt) = 2 cups (cups)
1 gram (g) = 1000 milligrams (mg) 1 quart (qt) = 2 pints (pt)
1 kilogram (kg) = 1000 grams (g) 1 gallon (gal) = 4 quarts (qt)
1 ounce (oz) = 28.35 grams (g). 1 cubic foot (ft³) = 7.481 gallons (gal)
1 pound (lb) = 0.454 kilograms (kg) 1 liter (l) = 1000 milliliters (ml)
1 cubic meter (m³) = 1000 liters (l)
1 gallon (gal) = 3.785 liters (l)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)

Explanation:

Step1: Convert grams to milligrams

Since \(1\ \text{g}=1000\ \text{mg}\), then \(810\ \text{g}=810\times1000 = 810000\ \text{mg}\)

Step2: Convert cubic feet to liters

We know that \(1\ \text{ft}^3 = 7.481\ \text{gal}\) and \(1\ \text{gal}=3.785\ \text{L}\). So \(1\ \text{ft}^3=7.481\times3.785\ \text{L}\)

$$7.481\times3.785=(7 + 0.481)\times(3+0.785)=7\times3+7\times0.785+0.481\times3+0.481\times0.785$$

$$=21+5.495+1.443+0.378=28.316\ \text{L}$$

Step3: Calculate the density in milligrams per liter

Density \(=\frac{810000\ \text{mg}}{28.316\ \text{L}}\approx28605\ \text{mg/L}\)

Answer:

\(28605\)