College

The outside of a closed glass display case measures 22 inches by 15 inches by 12 inches. The glass is half an inch thick. How much air is contained in the case?

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.