A rectangular box with a square base and no top is to be constructed. It must hold 32,000 in3. What are the dimensions of such a box that uses the smallest amount of material (i.e. that has the smallest surface area)?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.2: Perimeter And Area Of Polygons
Problem 38E: Examine several rectangles, each with an area of 36 in2, and find the dimensions of the rectangle...
icon
Related questions
Question
  1. A rectangular box with a square base and no top is to be constructed. It must hold 32,000 in3. What are the dimensions of such a box that uses the smallest amount of material (i.e. that has the smallest surface area)?

Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Area
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,