+0

0
2538
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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!

May 23, 2018

#1
+10435
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!

May 23, 2018
#2
+102320
+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

May 23, 2018
#3
+10435
0

I think that's the way it is.

May 23, 2018