A manufacturer is building a box with no top. The box is constructed from a piece of cardboard that is 10 inches long and 15 inches wide by cutting out the corners and folding up the sides. The manufacturer wants to build a box with maximum volume. What dimensions maximize the volume of the box, and what is that volume? A.  The maximum volume occurs when the box has dimensions of length 11 inches, width 6 inches, and height 2 inches. The maximum volume of the box is 132 cubic inches.   B.  The maximum volume occurs when the box has dimensions of length 11 inches, width 6 inches, and height 2 inches. The maximum volume of the box is 66 cubic inches.   C.  The maximum volume occurs when the box has dimensions of length 9 inches, width 4 inches, and height 3 inches. The maximum volume of the box is 108 cubic inches.   D.  The maximum volume occurs when the box has dimensions of length 9 inches, width 4 inches, and height 3 inches. The maximum volume of the box is 54 cubic inches.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
icon
Related questions
icon
Concept explainers
Question

A manufacturer is building a box with no top. The box is constructed from a piece of cardboard that is 10 inches long and 15 inches wide by cutting out the corners and folding up the sides. The manufacturer wants to build a box with maximum volume. What dimensions maximize the volume of the box, and what is that volume?

A.  The maximum volume occurs when the box has dimensions of length 11 inches, width 6 inches, and height 2 inches. The maximum volume of the box is 132 cubic inches.
 
B.  The maximum volume occurs when the box has dimensions of length 11 inches, width 6 inches, and height 2 inches. The maximum volume of the box is 66 cubic inches.
 
C.  The maximum volume occurs when the box has dimensions of length 9 inches, width 4 inches, and height 3 inches. The maximum volume of the box is 108 cubic inches.
 
D.  The maximum volume occurs when the box has dimensions of length 9 inches, width 4 inches, and height 3 inches. The maximum volume of the box is 54 cubic inches.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Application of Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry
Algebra and Trigonometry
Trigonometry
ISBN:
9781938168376
Author:
Jay Abramson
Publisher:
OpenStax
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning