A magnesium alloy contains the following volumes of each element: 341.2 cubic decimeters of magnesium, 30.96 cubic decimeters of aluminum, 488.0 cubic centimeters of manganese, and 672.0 cubic centimeters of zinc. Find the percent composition by volume of aluminum. Round the answer to the nearest hundredth percent.
To find the percent composition by volume of aluminum, we need to find the total volume of the magnesium alloy first. We have:
$341.2 + 30.96 + 488.0 + 672.0=1532.16$ cubic centimeters.
The percent composition by volume of aluminum is then:
$\frac{30.96\text { cubic decimeters (dm}^3\text {)}\times100}{1532.16\text { cubic centimeters (cm}^3\text {)}}=\boxed{2.02\%}$.
To find the percent composition by volume of aluminum in the magnesium alloy, we need to calculate the volume of aluminum as a fraction of the total volume of the alloy, and then convert it to a percentage.
First, let's find the total volume of the alloy:
Total Volume = Volume of Magnesium + Volume of Aluminum + Volume of Manganese + Volume of Zinc
Total Volume = 341.2 cubic decimeters + 30.96 cubic decimeters + 488.0 cubic centimeters + 672.0 cubic centimeters
Since the units are different (cubic decimeters and cubic centimeters), we need to convert one to match the other. Let's convert the volume of manganese from cubic centimeters to cubic decimeters.
Volume of Manganese = 488.0 cubic centimeters = 488.0 ÷ 1000 = 0.488 cubic decimeters
Now we can calculate the total volume of the alloy:
Total Volume = 341.2 cubic decimeters + 30.96 cubic decimeters + 0.488 cubic decimeters + 672.0 cubic centimeters
Total Volume = 342.688 cubic decimeters + 672.0 cubic centimeters
Next, let's calculate the percent composition of aluminum:
Percent Composition of Aluminum = (Volume of Aluminum ÷ Total Volume) × 100
Percent Composition of Aluminum = (30.96 cubic decimeters ÷ (342.688 cubic decimeters + 672.0 cubic centimeters)) × 100
Again, since the units are different, we need to convert the volume of aluminum from cubic decimeters to cubic centimeters.
Volume of Aluminum = 30.96 cubic decimeters = 30.96 × 1000 = 30960 cubic centimeters
Now we can calculate the percent composition of aluminum:
Percent Composition of Aluminum = (30960 cubic centimeters ÷ (342.688 cubic decimeters + 672.0 cubic centimeters)) × 100
Let's simplify and calculate the fraction first:
Percent Composition of Aluminum = (30960 cubic centimeters ÷ (342.688 cubic decimeters + 672.0 cubic centimeters)) × 100
Percent Composition of Aluminum = (30960 cubic centimeters ÷ 342.688 cubic decimeters + 672.0 cubic centimeters) × 100
Percent Composition of Aluminum = (30960 cubic centimeters ÷ 342.688 + 672.0 cubic centimeters) × 100
Percent Composition of Aluminum = (30960 cubic centimeters ÷ 342.688 cubic decimeters + 672.0 cubic centimeters) × 100
Percent Composition of Aluminum ≈ (30960 ÷ (342.688 + 672.0)) × 100
Percent Composition of Aluminum ≈ (30960 ÷ 1014.688) × 100
Percent Composition of Aluminum ≈ 30.51
Rounding to the nearest hundredth percent, the percent composition by volume of aluminum in the magnesium alloy is approximately 30.51%.
To find the percent composition by volume of aluminum in the magnesium alloy, we need to calculate the total volume of the alloy and then determine the ratio of the volume of aluminum to the total volume.
First, let's convert all the measurements to the same unit of volume. Since we need to find the percent composition by volume, it's best to use the same unit of volume for all elements. Let's convert the cubic decimeters to cubic centimeters.
1 cubic decimeter (dm³) = 1,000 cubic centimeters (cm³)
So, 341.2 cubic decimeters of magnesium = 341.2 * 1,000 = 341,200 cubic centimeters.
And 30.96 cubic decimeters of aluminum = 30.96 * 1,000 = 30,960 cubic centimeters.
Now, let's calculate the total volume of the alloy by adding the volumes of all the elements:
Total volume = volume of magnesium + volume of aluminum + volume of manganese + volume of zinc
Total volume = 341,200 cm³ + 30,960 cm³ + 488.0 cm³ + 672.0 cm³
Total volume = 373,320 cm³
Next, we can determine the ratio of the volume of aluminum to the total volume:
Percent composition of aluminum by volume = (Volume of aluminum / Total volume) * 100
Substituting the values:
Percent composition of aluminum by volume = (30,960 cm³ / 373,320 cm³) * 100
Now, let's calculate the result:
Percent composition of aluminum by volume ≈ (0.0829) * 100 ≈ 8.29%
Therefore, the percent composition by volume of aluminum in the magnesium alloy is approximately 8.29%.