Question

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. Find the surface area of each of your designs.

Answer 1

The surface area of each of your designs is $486 inches^{2}$ . 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 $6side^{2}$ .

⇒ $Area = 6(side)^{2}\\Area = 6(9)^{2}\\Area = 486 in^{2}$

Therefore, the surface area of each of your designs is $486 inches^{2}$ .