Question

How many baseballs with a diameter of 2.90inches, can fit into a box that is 48in x 40in x36in?

Answer 1

5413 baseballs

Step-by-step explanation:

Dimensions of the box = 48in x 40in x 36in.

The diameter of one baseball = 2.90 inches

Radius = Diameter ÷ 2 = 2.90 ÷ 2 =1.45 Inches

First, we find the volume of one of the baseball.

The baseball is in the shape of a sphere and:

`\text{Volume of a Sphere}=(4)/(3)\pi r^3`

Therefore, the volume of one baseball will be:

`\begin{gathered} =(4)/(3)*\pi*1.45^3 \\ =12.77in^3 \end{gathered}`

Next, we find the volume of the box.

`\begin{gathered} \text{Volume of the box}=48*40*36 \\ =69120in\text{.}^3 \end{gathered}`

Therefore, the number of baseballs that will fit into the box will be:

`\begin{gathered} \frac{\text{Volume of the box}}{Volume\text{ of one baseball}}=(69120)/(12.77)=5412.7 \\ \approx5413 \end{gathered}`