a three - dimensional model of lucias apartment is shown. to cool the whole apartment, an air conditioner…

Explanation:

Step1: Calculate volume of large - part

The large rectangular - part has dimensions (20\times10\times20). The volume (V_1) of a rectangular prism is (V = l\times w\times h), so (V_1=20\times10\times20 = 4000) cubic feet.

Step2: Calculate volume of small - part

The small rectangular - part has dimensions (16\times10\times(20 - 12)=16\times10\times8). Using the volume formula (V = l\times w\times h), (V_2=16\times10\times8 = 1280) cubic feet.

Step3: Calculate total volume

The total volume (V) of the apartment is (V = V_1+V_2=4000 + 1280=5280) cubic feet.

Step4: Calculate BTUs needed

Since 2.5 BTUs are needed per cubic foot, the total number of BTUs (N) is (N = 2.5\times V). Substituting (V = 5280) into the formula, we get (N=2.5\times5280 = 13200) (This is wrong as we mis - read the problem. Let's correct it).

The correct way: The apartment can be considered as two rectangular prisms. One with dimensions (20\times10\times20) and another with dimensions (16\times10\times12).

Step1: Calculate volume of first prism

The volume (V_1) of the first rectangular prism with (l = 20), (w = 10), (h = 20) is (V_1=20\times10\times20=4000) cubic feet.

Step2: Calculate volume of second prism

The volume (V_2) of the second rectangular prism with (l = 16), (w = 10), (h = 12) is (V_2=16\times10\times12 = 1920) cubic feet.

Step3: Calculate total volume

The total volume (V) of the apartment is (V=V_1 + V_2=4000+1920 = 7920) cubic feet.

Step4: Calculate BTUs needed

Since 2.5 BTUs are needed per cubic foot, the number of BTUs (N) is (N = 2.5\times V). Substituting (V = 7920) into the formula, (N=2.5\times7920=19800) BTUs.

Answer:

19,800 BTUs