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!
+12527 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!
+128407 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
