A rectangular piece of cardboard measuring 17 inches by 30 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) 12.18 in.
B) 14.7 in.
C) 3.49 in.
D) 24.35 in.

Question

Quizplus · Accepted Answer

The volume of the box, V, can be expressed as a function of x, where x is the length of the side of the square cut from each corner: V = x(17 - 2x)(30 - 2x). To find the value of x that maximizes the volume, we differentiate this function with respect to x and set the derivative equal to zero to solve for x. This yields a maximum volume at x ≈ 3.49 inches.

A Rectangular Piece of Cardboard Measuring 17 Inches by 30