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 calculate the total volume of the alloy and the volume of aluminum.
The total volume of the alloy is the sum of the volumes of all the elements:
Total volume = 341.2 cubic decimeters + 30.96 cubic decimeters + 488.0 cubic centimeters + 672.0 cubic centimeters
We will convert the units to cubic decimeters, since that is the unit used for the volume of aluminum:
Total volume = 341.2 cubic decimeters + 0.03096 cubic decimeters + 0.488 cubic decimeters + 0.672 cubic decimeters
Total volume = 342.41 cubic decimeters
Now we can calculate the percentage of aluminum by volume:
% composition of aluminum = Volume of aluminum / Total volume of the alloy * 100
% composition of aluminum = 0.03096 cubic decimeters / 342.41 cubic decimeters * 100
% composition of aluminum = 0.00990 * 100
% composition of aluminum = 0.99%
Rounded to the nearest hundredth percent, the percent composition by volume of aluminum is 0.99%.