Solve the problem.
-A rectangular piece of cardboard measuring 28 inches by 45 inches is to be made into a box with an open top by cutting equal-size squares from each corner and folding up the flaps. If the side length of each such square is x
Inches, for what value of x will the volume be a maximum? If necessary, round to the nearest hundredth.
A) 18.73 in.
B) 22.8 in.
C) 37.45 in.
D) 5.61 in.

Question

Quizplus · Accepted Answer

The volume of the box, V, can be expressed as a function of x: V = x(28 - 2x)(45 - 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, then solve for x. This yields a maximum volume at x = 5.61 inches, when rounded to the nearest hundredth.

Solve the Problem. -A Rectangular Piece of Cardboard Measuring 28 Inches by 45