Question

an air - conditioning system needed for a new warehouse is built in the shape of a rectangular prism. the warehouse is 250 feet long, 125 feet wide, and 22 feet high. a one - ton air conditioning unit can cool 12,000 cubic feet. what is the volume of the warehouse, and what size air conditioner is needed? the warehouse has cubic feet of space. the size air conditioner to be at least tons. select the correct answer from each drop - down menu. 79,000 31,250 687,500 750,000 reset next

Explanation:

Step1: Calculate the volume of the warehouse

The volume $V$ of a rectangular - prism is given by $V = l\times w\times h$, where $l = 250$ feet, $w = 125$ feet, and $h = 22$ feet. So $V=250\times125\times22$.
$V = 250\times(125\times22)=250\times2750 = 687500$ cubic feet.

Step2: Determine the size of the air - conditioner

A one - ton air - conditioning unit can cool 12000 cubic feet. Let the size of the air - conditioner be $x$ tons. Then $x=\frac{V}{12000}$. Substituting $V = 687500$ into the formula, we get $x=\frac{687500}{12000}\approx57.29$. Since we need to meet the cooling demand, we need to round up. So we need at least 58 tons, but we are just calculating the volume first.

Answer:

Volume: 687500 cubic feet, Size of air - conditioner: 58 tons (rounded up from $\frac{687500}{12000}$)