The surface area of each of your designs is [tex]486 inches^{2}[/tex] . So dimensions (in inches) of 4 different plastic shipping containers that would fit the boxes exactly is a cube of side 9 inches.
Step-by-step explanation:
Here we have , Olivia has to design a plastic shipping container that will hold 12 basketballs in individual boxes. The basketballs have a radius of 4.5 inches and fit exactly in their individual boxes that are cubes. Give the dimensions (in inches) of 4 different plastic shipping containers that would fit the boxes exactly. Two containers with the same dimensions in a different order do not count as different containers. Basketball is in form of sphere who's radius is 4.5 inches , also it's inscribed in cubes or boxes perfectly . In this case:
Side of a cube = 2(radius of sphere) = 2(4.5) = 9 in
We know that , surface area of a cube is [tex]6side^{2}[/tex] .
⇒ [tex]Area = 6(side)^{2}\\Area = 6(9)^{2}\\Area = 486 in^{2}[/tex]
Therefore, the surface area of each of your designs is [tex]486 inches^{2}[/tex] .
