Question

Determine the mass (in tons) of a cylinder with a volume of 25.0 m^3. (1 ton = 2000 lbs.) The density calculated in A1 (.002) is a conversion factor. Use dimensional analysis for all steps.

Answer 1

To determine the mass of a cylinder with a volume of 25.0 m^3 using dimensional analysis, you can use the following steps:

Step 1: Start with the given volume in cubic meters.

- Volume = 25.0 m^3

Step 2: Use the density conversion factor to convert from cubic meters to cubic feet. Since 1 m^3 = 35.3147 cubic feet, we can write:

- 25.0 m^3 * (35.3147 ft^3 / 1 m^3) = 882.8675 ft^3

Step 3: Now, we need to convert from cubic feet to pounds using density.

- Density (D) = 0.002 lb/ft^3 (given conversion factor)

- Mass (M) = Volume (V) * Density (D)

- M = 882.8675 ft^3 * 0.002 lb/ft^3 = 1.765735 lb

Step 4: Finally, convert the mass from pounds to tons using the given conversion factor of 1 ton = 2000 lbs:

- Mass (M) = 1.765735 lb * (1 ton / 2000 lb) = 0.0008828675 tons

So, the mass of the cylinder with a volume of 25.0 m^3 is approximately 0.0008828675 tons.

Answer 2

Step-by-step explanation:

The answer is 1. Start with the given volume of the cylinder: 25.0 m^3.

2. Use the density conversion factor (given as 0.002 in A1) to convert from volume to mass. Since density is mass per unit volume, we can set up a conversion factor as follows:

- 0.002 tons / 1 m^3 (or 2000 lbs / 1 m^3)

3. Multiply the volume (25.0 m^3) by the conversion factor:

- 25.0 m^3 * 0.002 tons / 1 m^3 = 0.05 tons

4. The mass of the cylinder is 0.05 tons.

To summarize, the mass of the cylinder with a volume of 25.0 m^3 is 0.05 tons.