An open box is to be constructed from a square sheet of cardboard measuring 30 centimetres by 30 centimetres. This is done by cutting out the shaded square areas indicated on the the diagram below, then folding along the dotted lines and then gluing the sides together. Find what dimension x will maximise the volume of the box and the corresponding maximum volume. 30 30 x x
An open box is to be constructed from a square sheet of cardboard measuring 30 centimetres by 30 centimetres. This is done by cutting out the shaded square areas indicated on the the diagram below, then folding along the dotted lines and then gluing the sides together. Find what dimension x will maximise the volume of the box and the corresponding maximum volume. 30 30 x x
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 43PS
Related questions
Question
Solve without the use of a calculator
![An open box is to be constructed from a square sheet of cardboard measuring 30 centimetres
by 30 centimetres. This is done by cutting out the shaded square areas indicated on the
the diagram below, then folding along the dotted lines and then gluing the sides together.
Find what dimension x will maximise the volume of the box and the corresponding maximum
volume.
30
30
x
x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82646c21-62ab-4b29-8f2b-e38f8c8da55e%2Fa2850bfb-f587-491b-bb7a-7e15cd150f28%2Fjdo5qtv_processed.png&w=3840&q=75)
Transcribed Image Text:An open box is to be constructed from a square sheet of cardboard measuring 30 centimetres
by 30 centimetres. This is done by cutting out the shaded square areas indicated on the
the diagram below, then folding along the dotted lines and then gluing the sides together.
Find what dimension x will maximise the volume of the box and the corresponding maximum
volume.
30
30
x
x
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Algebra for College Students](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Algebra: Structure And Method, Book 1](https://www.bartleby.com/isbn_cover_images/9780395977224/9780395977224_smallCoverImage.gif)
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
![Elementary Algebra](https://www.bartleby.com/isbn_cover_images/9780998625713/9780998625713_smallCoverImage.jpg)
Elementary Algebra
Algebra
ISBN:
9780998625713
Author:
Lynn Marecek, MaryAnne Anthony-Smith
Publisher:
OpenStax - Rice University