To keep heating costs down for a structure, architects want the ratio of surface area to volume as small as possible. An expression for the ratio of the surface area to volume for the square prism shown is 2b+4h/bh Find the ratio when b=15 ft and h=10 ft.
To find the ratio of surface area to volume, we plug in the values for b and h into the expression:
Surface Area = 2b^2 + 4bh
Volume = b^2h
Ratio = (2b^2 + 4bh) / (b^2h)
When b = 15 ft and h = 10 ft:
Surface Area = 2(15)^2 + 4(15)(10) = 2(225) + 4(150) = 450 + 600 = 1050 ft^2
Volume = (15)^2(10) = 225(10) = 2250 ft^3
Ratio = 1050 / 2250 = 0.4666666666666667
Therefore, when b = 15 ft and h = 10 ft, the ratio of surface area to volume for the square prism is 0.4667.