Question

a metal warehouse, whose dimensions are shown below, needs paint. the front and back of the warehouse each have 2 rollup doors measuring 22 ft by 28 ft each. the side of the warehouse facing the parking lot has an entry door measuring 63 in by 80 in. the other side of the warehouse has no window or door. use the given information to answer the questions. each tab shows a different view of the warehouse. front - right view back - left view conversion facts for length 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 yard (yd) = 36 inches (in) (a) assuming the roof and doors require no paint, what is the area in square feet that needs paint? (do not round any intermediate computations and give your answer as a whole number.) (b) the paint to be used is sold in cans. each can contains enough paint to cover 580 ft². assume

Explanation:

Step1: Calculate the total area of the four walls

The formula for the lateral surface area of a rectangular prism (warehouse) is \(2\times(\text{length}\times\text{height}+\text{width}\times\text{height})\).
Here, length \(l = 50\) ft, width \(w=43\) ft, height \(h = 35\) ft.
The total area of the four walls \(A_{walls}=2\times(50\times35 + 43\times35)\)

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Step2: Calculate the area of the roll - up doors

Each front and back has 2 roll - up doors. So in total, there are \(2\times2 = 4\) roll - up doors.
Each roll - up door has an area of \(A_{door1}=22\times28\) ft².
The total area of the roll - up doors \(A_{roll - up}=4\times22\times28\)

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Step3: Calculate the area of the entry door

The entry door has dimensions \(63\) in by \(80\) in. Convert inches to feet: \(63\div12=\frac{63}{12}=\frac{21}{4}\) ft and \(80\div12=\frac{80}{12}=\frac{20}{3}\) ft.
The area of the entry door \(A_{door2}=\frac{21}{4}\times\frac{20}{3}\)

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Step4: Calculate the area to be painted

The area to be painted \(A = A_{walls}-A_{roll - up}-A_{door2}\)

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Answer:

\(4011\)