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Answer :
Answer:
V_air = V_inside = 2,600 cubic inches.
Step-by-step explanation:
To find the amount of air contained in the display case, we need to subtract the volume of the glass from the volume of the outside dimensions.
The volume of the outside dimensions of the display case is:
V_outside = 22 * 15 * 12 = 3,960 cubic inches
The glass is half an inch thick, which means it adds 1 inch to each dimension of the display case. Therefore, the inside dimensions of the display case are:
22 - 2(1) = 20 inches
15 - 2(1) = 13 inches
12 - 2(1) = 10 inches
The volume of the inside dimensions of the display case is:
V_inside = 20 * 13 * 10 = 2,600 cubic inches
The volume of the glass is the difference between the outside and inside volumes:
V_glass = V_outside - V_inside = 3,960 - 2,600 = 1,360 cubic inches
Therefore, the amount of air contained in the display case is:
V_air = V_inside = 2,600 cubic inches.
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