Given the box of popcorns and the cone of popcorns, you can assume that the box is a rectangular prism.
You can use this formula to calculate the volume of the box:
[tex]V_{r.prism}=lwh[/tex]
Where "l" is the length, "w" is the width, and "h" is the height.
In this case:
[tex]\begin{gathered} l=5\text{ }in \\ w=3\text{ }in \\ h=6\text{ }in \end{gathered}[/tex]
Using the formula, you get:
[tex]V_{r.prism}=V_{box}=(5\text{ }in)(3\text{ }in)(6\text{ }in)=90\text{ }in^3[/tex]
Use this formula to calculate the volume of the cone:
[tex]V_{cone}=\frac{\pi r^2h}{3}[/tex]
Where "r" is the radius and "h" is the height.
In this case (knowing that the radius is half the diameter):
[tex]\begin{gathered} r=\frac{6\text{ }in}{2}=3\text{ }in \\ \\ h=8\text{ }in \\ \\ \pi\approx3.14 \end{gathered}[/tex]
Then, you get:
[tex]V_{cone}=\frac{(3.14)(3in)^2(8in)}{3}\approx75.36\text{ }in^3[/tex]
Subtract the volume of the cone from the volume of the box, in order to determine how much more the box holds than the cone:
[tex]90\text{ }in^3-75.36\text{ }in^3=14.64\text{ }in^3[/tex]
Hence, the answer is:
[tex]14.64\text{ }in^3[/tex]
