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Zorluk: Çok zorRectangular Area Applications

A commercial painting crew is hired to paint the four exterior walls of a rectangular warehouse. The warehouse has a length of 120 ft120\text{ ft}, a width of 80 ft80\text{ ft}, and a height of 24 ft24\text{ ft}. The building features 22 identical loading doors, each measuring 16 ft16\text{ ft} wide by 15 ft15\text{ ft} high, and 44 identical windows, each measuring 6 ft6\text{ ft} wide by 5 ft5\text{ ft} high. The doors and windows will not be painted. The crew must apply exactly 22 coats of paint to all paintable exterior wall surfaces. If one gallon of paint covers exactly 400 square feet400\text{ square feet}, how many total gallons of paint are required for this project?

Cevap: 45 gallons

Cevap

45
The total area of the four exterior walls is 9,600 sq ft. The doors and windows have a combined area of 600 sq ft, leaving a net paintable area of 9,000 sq ft per coat. Since two coats are required, the total area to cover is 18,000 sq ft. With each gallon covering 400 sq ft, dividing 18,000 by 400 gives exactly 45 gallons.

Adım Adım Çözüm

1
Calculate the gross area of the four exterior walls.
9,600 sq ft
To find the total surface area before accounting for doors and windows.
2
Calculate the total area of the unpainted cutouts.
600 sq ft
The doors and windows will not be painted and must be subtracted.
3
Determine the net paintable area for a single coat.
9,000 sq ft
Subtracting the cutout area from the gross area gives the actual area to paint.
4
Calculate the total area to be covered for two coats.
18,000 sq ft
The problem specifies that exactly two coats of paint must be applied.
5
Determine the total gallons of paint required.
45
Divide the total area to be painted by the coverage rate of 400 sq ft per gallon.

Anahtar Kavram

Calculating net rectangular area by subtracting cutouts and applying a rate for multiple layers.
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Rectangular Area Applications

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