A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 168 inches. Write a function that represents the volume of the package. A)V(x) = - 4x²(42 + x) B)V(x) = 4x²(42 + x) C)V(x) = 4x²(42 - x) D)V(x) = 4x²(-42 - x) E)V(x) = - 4x²(42 - x)

Question

Quizplus · Accepted Answer

The formula for volume of a rectangular package is V = lwh. Since the package is rectangular and we are given the maximum combined length and girth, we know that the package must be a square prism. Let x be the length of one side of the cross section. Then the perimeter of the cross section is 4x, and we are given that the maximum combined length and girth is 168 inches, so we have the equation 4x + 2x = 168, which simplifies to 6x = 168, or x = 28. Therefore, the length, width, and height of the package are all 28 inches. So the volume is V = lwh = 28*28*28 = 21952 cubic inches. Using the answer choices, we can see that only choice C gives us the correct expression for this volume.

A Rectangular Package to Be Sent by a Delivery Service