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\tvolume
1 pound (lb) = 16 ounces (oz)\t1 cup (cup) = 8 fluid ounces (fl oz)
1 ton (ton) = 2000 pounds (lb)\t1 pint (pt) = 2 cups (cups)
1 gram (g) = 1000 milligrams (mg)\t1 quart (qt) = 2 pints (pt)
1 kilogram (kg) = 1000 grams (g)\t1 gallon (gal) = 4 quarts (qt)
1 ounce (oz) = 28.35 grams (g)\t1 cubic foot (ft²) = 7.481 gallons (gal)
1 pound (lb) = 0.454 kilograms (kg)\t1 liter (l) = 1000 milliliters (ml)
\t1 cubic meter (m³) = 1000 liters (l)
\t1 gallon (gal) = 3.785 liters (l)
\t1 fluid ounce (fl oz) = 29.574 milliliters (ml)

Explanation:

Step1: Convert grams to milligrams

Since \(1\) gram \( = 1000\) milligrams, then \(810\) grams \(=810\times1000 = 810000\) milligrams.

Step2: Convert cubic feet to liters

We know that \(1\) cubic foot \(=7.481\) gallons and \(1\) gallon \( = 3.785\) liters.
So, \(1\) cubic foot \(=7.481\times3.785\) liters.

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

$$=21+5.495+1.443+0.378=28.316$$

liters (approx).

Step3: Calculate the density in milligrams per liter

Density \(=\frac{\text{mass in milligrams}}{\text{volume in liters}}\)
Density \(=\frac{810000}{28.316}\approx28605\) (using a calculator for \(\frac{810000}{28.316}\))

Answer:

\(28605\)