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An alloy (solution of metals) is 80% by volume iron. The rest is aluminum. Aluminum has a density of 2.70 g/cm³, and iron's is 7.87 g/cm³. A block of alloy measures 2.0 ft. wide and 3.0 ft. long. If the block contains 25.8 pounds of aluminum, how thick is the block?

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To find out the thickness of the block, we can use the information given about the volume and the density of aluminum.

1. First, let's convert the dimensions of the block from feet to centimeters. Since 1 foot is equal to 30.48 centimeters, the width would be 2.0 ft * 30.48 cm/ft = 60.96 cm, and the length would be 3.0 ft * 30.48 cm/ft = 91.44 cm.

2. Next, let's calculate the volume of the alloy block. The volume of a rectangular block can be calculated by multiplying its length, width, and thickness. Let's assume the thickness of the block is "t".

Volume = Length * Width * Thickness
Volume = 91.44 cm * 60.96 cm * t

3. Since 80% of the volume of the alloy is iron, the remaining 20% must be aluminum. So, let's calculate the volume of aluminum in the block.

Volume of Aluminum = 0.20 * Total Volume

4. We know that density = mass / volume. Rearranging the formula, mass = density * volume. Given that the mass of aluminum is 25.8 pounds and the density of aluminum is 2.70 g/cm³, we can calculate the volume of aluminum using its mass and density.

Volume of Aluminum = Mass of Aluminum / Density of Aluminum

5. Now, let's equate the volume of aluminum calculated in step 4 to the volume calculated in step 3.

0.20 * Total Volume = Mass of Aluminum / Density of Aluminum

6. We can now substitute the known values and solve for Total Volume.

0.20 * (91.44 cm * 60.96 cm * t) = 25.8 pounds / 2.70 g/cm³

7. Convert the weight from pounds to grams (1 pound = 453.592 grams) and divide by the density of aluminum in g/cm³.

0.20 * (91.44 cm * 60.96 cm * t) = (25.8 pounds * 453.592 g/pound) / 2.70 g/cm³

8. Solve the equation for Total Volume.

Total Volume = [(25.8 pounds * 453.592 g/pound) / 2.70 g/cm³] / [0.20 * (91.44 cm * 60.96 cm)]

9. Finally, calculate the thickness of the block by solving for "t" in the equation obtained in the previous step.

t = Total Volume / (91.44 cm * 60.96 cm)

By following these steps, you can calculate the thickness of the alloy block.