Question

SportBounceCo makes and packages balls for different sports. Use your knowledge of polynomials to help the company design the box for one of its products. Which ball did you select? What do you know about the base of the box?

Answer 1

A cube will house each spherical ball.

The cube that houses a spherical ball will have side lengths equal to the diameter of the sphere.

We will need to find the surface area of the cube that houses the volleyball. The surface area of a cube is found by the formula:

`6a^2`

Where

a is the side length of the cube

First VolleyBall

Diameter = 8 inches

So, Cube Side Length = 8

Surface Area of Cube:

`\begin{gathered} 6a^2 \\ =6(8)^2 \\ =384 \end{gathered}`

So, Amount of Material Needed = 384 sq. in.

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Second VolleyBall

Diameter = 9 inches

So, Cube Side Length = 9

Surface Area of Cube:

`\begin{gathered} 6a^2 \\ =6(9)^2 \\ =486 \end{gathered}`

So, Amount of Material Needed = 486 sq. in.

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Third VolleyBall

Diameter = 10 inches

So, Cube Side Length = 10

Surface Area of Cube:

`\begin{gathered} 6a^2 \\ =6(10)^2 \\ =600 \end{gathered}`

So, Amount of Material Needed = 600 sq. in.

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Thus, the total amount of material needed to make 3 boxes for the volleyballs is 384 + 486 + 600 = 1470 square inches.