A rectangular piece of cardboard measuring 15 inches by 29 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.
A) 13.79 in.
B) 3.15 in.
C) 11.52 in.
D) 23.04 in.

Question

Quizplus · Accepted Answer

The volume of the box, V, can be expressed as a function of x: V = x(15 - 2x)(29 - 2x). To find the maximum volume, we differentiate this function with respect to x and set the derivative equal to zero to solve for x. This yields the value of x that maximizes the volume. Through this process, we find that x ≈ 3.15 inches maximizes the volume of the box.

A Rectangular Piece of Cardboard Measuring 15 Inches by 29