Answer:
5413 baseballs
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:
[tex]\text{Volume of a Sphere}=\frac{4}{3}\pi r^3[/tex]Therefore, the volume of one baseball will be:
[tex]\begin{gathered} =\frac{4}{3}\times\pi\times1.45^3 \\ =12.77in^3 \end{gathered}[/tex]Next, we find the volume of the box.
[tex]\begin{gathered} \text{Volume of the box}=48\times40\times36 \\ =69120in\text{.}^3 \end{gathered}[/tex]Therefore, the number of baseballs that will fit into the box will be:
[tex]\begin{gathered} \frac{\text{Volume of the box}}{Volume\text{ of one baseball}}=\frac{69120}{12.77}=5412.7 \\ \approx5413 \end{gathered}[/tex]