Question

Beverly needs to make a container in the shape of a rectangular prism that holds 1000 in3 of liquid. The height of the container must be 10 in. She wants to use the dimensions that will allow her to use the least amount of material possible. Beverly’s mother says the difference in the amount of material will be too minor to worry about. Beverly believes it is possible to save more than half the material needed if they pick the right dimensions. Who is correct? Support your answer with specific numbers, and explain your reasoning. The dimensions are measured in whole units.

Answer 1

Given:
volume = 1,000 in³
height = 10 in

1,000 in³ / 10 in = 100 in² Area.

100 in²

Length     Width        Surface Area of the Rectangular prism
100 in          1 in                       2,220 in²
  50 in          2 in                       1,240 in²
  25 in          4 in                          780 in²
  20 in          5 in                          700 in²
  

Surface area = 2(wl + hl + lw)

The best dimension is 20 inches by 5 inches by 10 inches. It has lesser surface area than other dimensions. Thus, it can save more materials.