A house with ceilings that are 2.4 meters high has five rectangular rooms with the following dimensions: 4 meters 3 5 meters; 4 meters 3 4 meters; 6 meters 3 4 meters; 6 meters 3 6 meters; and 6 meters 3 5.5 me-ters. Which of the following air conditioners will be adequate to cool this house: an 18,000-Btu unit that will cool 280 cubic meters; a 21,000-Btu unit that will cool 340 cubic meters; or a 24,000-Btu unit that will cool 400 cubic meters?

A 21,000-Btu unit that will cool 340 cubic meters;

Step-by-step explanation:

Calculating the volume of the five rooms, we have;

Room 1:

Volume = 2.4 *4*5

             = 48 m³

Room 2:

Volume = 2.4*4*4

              = 38.4 m³

Room 3:

Volume = 2.4*6*4

             =57.6 m³

Room 4:

Volume = 2.4*6*6

             =86.4 m³

Room 5:

Volume = 2.4*6*5.5

             = 79.2 m³

Total volume of the room = 48 +38.4 + 57.6 + 86.4 + 79.2

                                           = 309.6 m³

From the total volume obtained above, the air condition that will be adequate to cool the house is  21,000-Btu unit since the obtained volume(309.6 m³) is within the range of the specify volume (340 cubic meters).

This is more of a business application.  

Suppose that you want have a factory that produces boxes and you for every box your company can only use, let’s say 10cm^2 , in order for your company to be competitive on the market and beat competitors you want to produce boxes with as much storing capacity as possible, you can find the dimension of that box with maximum capacity using critical points for the volume function of the desired box.