Kepler’s wine barrel Several mathematical stories originated with the second wedding of the mathematician and astronomer Johannes Kepler. Here is one: While shopping for wine for his wedding, Kepler noticed that the price of a barrel of wine (here assumed to be a cylinder) was determined solely by the length d of a dipstick that was inserted diagonally through a centered hole in the top of the barrel to the edge of the base of the barrel (see figure). Kepler realized that this measurement does not determine the volume of the barrel and that for a fixed value of d, the volume varies with the radius r and height h of the barrel. For a fixed value of d, what is the ratio r/h that maximizes the volume of the barrel?
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Student Solutions Manual, Single Variable for Calculus: Early Transcendentals
Additional Math Textbook Solutions
Precalculus (10th Edition)
Glencoe Math Accelerated, Student Edition
Calculus & Its Applications (14th Edition)
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
- A single-threaded (or single-start) square-thread screw is shown in Figure 5-6. The lead of a screw is the distance that the screw advances in one turn (revolution). The lead is equal to the pitch in a single-threaded screw. Given the number of turns and the amount of screw advance, determine the leads.arrow_forwardConsidering that the consecutive dials on the natural gas meter rotate in opposite directions, what is the current reading in cubic feet of usage? The initial direction is clockwise.arrow_forwardSolve the right triangle shown at the right for all unknown sides and angles.arrow_forward
- Refer to the shaft shown in Figure 6-4. Determine the missing dimensions in the table using the dimensions given. All dimensions are in inches.arrow_forwardHow many feet off the ground are Al and Betty at each of the following times: a. 5 seconds after passing the 3 o’clock position? b. 10 seconds after passing the 3 o’clock position? c. 12 seconds after passing the 3 o’clock position? SHOW YOUR WORK!!arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
- Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning