Please answer the following questions, thanks! An open-top box is to be made by

Question

Please answer the following questions, thanks!

An open-top box is to be made by cutting squares from the corners of a 12 inch by 12 inch sheet of cardboard and bending up the sides. How large should the squares be in order to give the box a maximum volume? Make sure you understand this problem by Drawing a picture of t he situation. Labeling all of the given information. Listing the equation for the volume of a box. Make a plan for solving this problem by Writing the equation for the volume of the box in terms of one variable. Determining the domain for the volume function that meets all conditions. Find the solution for this problem by Finding the critical values of the volume function. Identifying which value gives the maximum volume. Give and check your answer for this problem.

Explanation / Answer

Solution:

If assume that started with a square 12" by 12"

From that you cut away four squares that were x" by x"

The volume is (12-2x)*(12-2x)*(x) = 144x - 48x2 - 4x3

So dV/dx = -12x2 - 96x + 144

Take Equal To 0

-12x2 - 96x + 144 = 0

Divide both sides by -12

x2 + 8x - 12 = 0

(x - 6) * ( x - 2) = 0

So x = 2 and x = 6

Burt if you cut off 6 inch squares the other dimensions would not exist.

So x = 2.

Therefore Volume = 2 * 8 * 8 = 128 cubic inches.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---