**Problem:**

You need to make an open-top box from a rectangle of cardboard 9 by 13 inches by cutting a square from each corner and folding up the sides. You want the box to have the maximum possible volume. Complete the following problems **showing all your work**:

If each square you cut out is x by x inches, write an expression for the volume of the box, V(x), in terms of x. A sketch may help. **Show all your work.**

**Sketch (or use technology to plot)** the function to find the maximum. **Clearly label** or state the (x,y) coordinates of the value of x that optimizes the function and the maximum Volume (y)

**How many dollars worth** of quarters (25 cent pieces) would it take to fill the box? **Show all your work!**

Guest May 23, 2018

#1**0 **

You need to make an open-top box from a rectangle of cardboard 9 by 13 inches by cutting a square from each corner and folding up the sides. You want the box to have the maximum possible volume. Complete the following problems showing all your work:

**Unfortunately, I do not know the diameter and height of a 25-cent pieces!**

Omi67 May 23, 2018

#2**+1 **

A quarter has a diameter of 24.26 mm ≈ .955 in

And the height (thickness) is 1.75 mm ≈ .0689 in

So....the volnme of one quarter is the volume of a cylinder with a diameter of 955 in and a height of .0689 in =

pi ( .955/2)^2 * ( .0689) ≈ .04935 in^3

So (theoretically), the number of quarters that would fit in the box is ≈ 182.876 in^3 / .04935 in^3 ≈ 3706 quarters

CPhill May 23, 2018