An apartment complex has a floor plan with dimensions shown. To effectively air condition a room, 20 BTU’s are required for every square foot. Determine the minimum BTU’s required for an air conditioner to cool the room effectively. Round the answer to the nearest 100 BTU’s.

Question

Middle School

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Answer :

rahulnair123437 rahulnair123437 · Answer 1 · 2024-07-10T20:12:24-04:00

12,900 BTU's are required to cool the room effectively.

Step-by-step explanation:

Step 1:

We must calculate the area of the entire shape to determine the minimum BTU's required to cool the room effectively.

It is made up of a semi-circle a rectangle, and a trapezoid.

Step 2:

The area of a semi-circle [tex]=\frac{ \pi r^{2} }{2} .[/tex]

Here, the diameter is 20 feet so the radius is 10 feet.

The area of the semi-circle [tex]=\frac{ \pi r^{2} }{2} =\frac{ (\pi) (10^{2}) }{2} = 157.079[/tex] square feet.

The area of a rectangle [tex]= (l)(w).[/tex]

The length of the rectangle is 22 feet and the width is 20 feet.

The area of a rectangle [tex]= (l)(w) =(22)(20) = 440[/tex] square feet.

The area of a trapezoid [tex]=\frac{a+b}{2} (h).[/tex]

Here [tex]a=12, b= 20, h= 3[/tex].

The area of a trapezoid [tex]=\frac{12+20}{2} (3) = 48[/tex] square feet.

Step 3:

The total area of the floor plan [tex]=157.079+440+48 = 645.079[/tex] square feet.

If 20 BTU's are required for a single square foot,

The number of BTU's for 645.079 square feet [tex]= (645.079)(20)=12,901.58[/tex] BTU's.

Rounding this off, we get 12,900 BTU's required to cool the room effectively.