Iron has a density of 7.87 g/cm\(^3\). How many pounds does 2.80 cubic feet of iron weigh?

- Conversion factors: 453.6 g = 1 lb, 2.54 cm = 1 in, and 1 ft = 12 in.

How many pounds does 49.0 in\(^3\) of gold weigh?

- The density of gold is 19.3 g/cm\(^3\).

- Conversion factors: 2.54 cm = 1 in, and 454 g = 1 lb.

20 drops of an essential oil have a mass of 600.8 mg and a density of 0.875 g/cm\(^3\). What is the volume occupied by the drops?

Suppose a piece of paper is 0.0084 cm thick. How many atoms span the thickness if the radius of the atom is 2.95 angstroms?

- Conversion: 1 angstrom = 10\(^{-10}\) m.

What is the area in square meters of a piece of tin foil with a mass of 254 g and a thickness of 26016 nm?

- The density of tin (Sn) is 5.75 g/cm\(^3\).

- Conversion: 1 nm = 10\(^{-7}\) cm.

- Formula: Volume = length x width x height; Area = length x width.

These problems all involve using density and other conversion factors to solve calculations involving volume, mass, and number of particles. The answers for the weight of 2.80 cubic feet of iron and 49.0 in of gold are approximately 1303.37 lbs and 886.5 lb respectively. The volume occupied by 20 drops of essential oil is approximately 0.687 cm³, there are approx 285 atoms spanning the thickness of a piece of paper, and the area of the piece of tin foil is approx 0.44 square meters.

Explanation:

Tackling each of these problems separately:

1) To calculate the weight of iron, you have to use the density to convert the volume to mass and then convert the mass to pounds. The result is approximately 1303.37 lbs.

2) For the gold, using similar steps as the iron calculation, the weight comes out to be around 886.5 lb.

3) For essential oil, you can calculate the volume by dividing the mass by the density. The result is approximately 0.687 cm³.

4) To find the number of atoms in the thickness of a piece of paper, you need to first convert the given measurements to a common unit (like angstroms) and then find the number of 'atom-widths' that fit into the thickness of a piece of paper. The answer is approximately 285 atoms.

5) For the tin foil, you'll use the volume formula to first calculate the volume and then using the area formula, you can calculate the area of the tin foil, given the thickness and the mass. The answer is approximately 0.44 square meters.

Learn more about Density Calculations here:

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