ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Graphing Calculator - Finding Maximum Volume

Updated on December 8, 2011

Ok, most of the algebra we learn in school isn’t really that useful. Some math teachers probably disagree with this but being a math teacher, I am allowed to say it! I mean really, as I said in my first problem of this little series, how many people really have added x’s and y’s since they left school.

Anyway, this is another little problem that might be of interest to some. Suppose you have a 4’ x 8’ piece of plywood. What is the maximum volume box you can make without a top? With the help of a graphing calculator, we can easily solve this problem.

The answer is found similar to the area problem. Think of unfolding the box into the following pattern.

Volume = length x width x height

= x(8 – 2x)(4 – 2x)

Are we going to do this algebraically? Not on your life! Zip over to http://webgraphing.com/graphing_basic.jsp and plug the formula into the graphing calculator just as it is written above. Click on Graph It and you should get the following graph. I have shaded in the part we want to look at. We don’t care about the negative part because you can’t have a negative length and width!

If you check out the table below, you can see the local maximum (maximum volume in this case) is 12.32 cubic feet for an x value of 0.85. So that means if our box is 0.85 feet by 4 – 2(0.85) feet by 8 -2(0.85) feet, we will have the largest possible volume. You don't have to understand the table to find the numbers!

Therefore, 10” x 27.5” x 75.5” gives us a maximum volume of 12.32 cubic feet, the biggest that is possible from a piece of plywood. Of course, if you are really doing this, you would need to allow a little less here and there for the thickness of the plywood! But this gives you a pretty good idea.

You can extend this same idea to a box with a lid, or a metal cylinder with or without a top and bottom. I’ll write about those two in a later lesson. It is a fairly simple way, with the help of a graphing calculator, to find the maximum volume of any shape you can cut out of a given piece of material.

Comments

    0 of 8192 characters used
    Post Comment

    • kirbylau profile image

      kirbylau 6 years ago from Wuhan, China

      I concur

    • Storytellersrus profile image

      Barbara 6 years ago from Stepping past clutter

      Any time, Teach!

    • Steve LePoidevin profile image
      Author

      Steve LePoidevin 6 years ago from Thailand

      Thanks for stopping by and glad you enjoyed it!

    • Storytellersrus profile image

      Barbara 6 years ago from Stepping past clutter

      Thank God there are people out there who actually keep math alive, lol. I certainly am not a practitioner. I avoid balancing my checkbook if at all possible. I do love to play math games in my head, however. Maybe not the calculator kind, but addition. I like figuring out things without using pad and paper. I suppose this comes from my father, who was pretty brilliant in math.

      Anyway, I think it is fun to read over these hubs and consider practical applications, like volume. This does come in useful. I too often eyeball it, lol. Great job. Voted up and interesting.

    • profile image

      卓峰 6 years ago

      Like! Suggestion: do this problem using Calculus

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)