Question

Ben is building a workshop in his backyard with dimensions as shown in the figure. Ben is planning to air-condition the workshop using a window-unit air conditioner. He needs to determine the BTU's (British Thermal Units) required to cool the building. For a new construction with good insulation, there should be 2 BTU per cubic foot. What is the minimum capacity for the window air conditioner that Ben need to purchase.

Answer 1

2160 BTU

Explanation:

Ben looks at his plan and realizes that his building can be viewed as a triangular prism sitting on a cube.

Calculating the volume of a cube is easy… Length x Width x Height (LWH)… so 12 x 10 x 8 = 120 x 8 = 960 cubic feet for the cube part.

For the prism, it’s almost the same… but divided by 2 : (LWH)/2, so… (12 x 10 x 2) / 2 = (120 x 2) / 2 = 240 / 2 = 120 cubic feet for the prism part.

Total for the building : 960 + 120 = 1080 cubic feet

Since 2 BTU per cubic foot, the power of the unit needs to be at least 1080 x 2 = 2160 BTU.