Question

A movie theater sells two sizes ofpopcorn. How much more doesthe box hold than the cone?

Answer 1

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:

`V_(r.prism)=lwh`

Where "l" is the length, "w" is the width, and "h" is the height.

In this case:

`\begin{gathered} l=5\text{ }in \\ w=3\text{ }in \\ h=6\text{ }in \end{gathered}`

Using the formula, you get:

`V_(r.prism)=V_(box)=(5\text{ }in)(3\text{ }in)(6\text{ }in)=90\text{ }in^3`

Use this formula to calculate the volume of the cone:

`V_(cone)=(\pi r^2h)/(3)`

Where "r" is the radius and "h" is the height.

In this case (knowing that the radius is half the diameter):

`\begin{gathered} r=\frac{6\text{ }in}{2}=3\text{ }in \\ \\ h=8\text{ }in \\ \\ \pi\approx3.14 \end{gathered}`

Then, you get:

`V_(cone)=((3.14)(3in)^2(8in))/(3)\approx75.36\text{ }in^3`

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:

`90\text{ }in^3-75.36\text{ }in^3=14.64\text{ }in^3`

Hence, the answer is:

`14.64\text{ }in^3`