Question

Week 7 (Differentiation) This response should be no longer than 1 M page (not including diagrams or tables). This response relates to criterion 1 (mathematical understanding), criterion 3 (problem solving and reasoning skills, and criterion 4 (communication of mathematics) in the grading rubric for this assessment task. Think back to the box creation activity during the workshop. In this activity, we used an A4 sheet of paper to create an open box that would hold the maximum volume. For this week's folio task, you are required, once again, to create an box that you will use to transport the maximum amount of Rhodium (much more precious than gold) from the mine to your house. The following are your instructions: • You have an A3 sheet of cardboard from which you are to create an open box • Find the dimensions of the open box that will hold the maximum volume of Rhodium • Show all working including diagrams) on how you obtained these dimensions Show that they dimensions you calculate will actually hold the MAXIMUM volume possible, given the restrictions

Answer 1

volume of open box made from Rectangle sheet Calt out with squares lo re 2 8 Ix height Fx 827 10- 2x volume V(x) = XC8-201) (10-2x) 8-27 can't be negative 8-28 must greater than zero 8-21 > 8> 2x Gay) 10-20 lo zu x 25 and also x must be greater than zero graph V(X) $ 45 here is the a value must blw the oand u restricted domain is 2014) maximum volume the middle value of the domain grues maximum volume. here (X=2 length=6 width 4

These are restrictions for creating the open box with having maximum volume.

This procedure is same for any dimensions of rectangle sheet.