Concept explainers
Comparing American and rugby union footballs An ellipse centered at the origin is described by the equation
- a. Use the washer method to find the volume of an ellipsoid (in terms of a and b). Check your work using the shell method.
- b. Both American and rugby union footballs have the shape of ellipsoids. The maximum regulation size of a rugby union football corresponds to parameters of a = 6 in and b = 3.82 in, and the maximum regulation size of an American football corresponds to parameters of a = 5.62 in and b = 3.38 in. Find the volume of each football.
- c. Fill in the blank: At their maximum regulation sizes, the volume of a rugby union football has approximately _____ times the volume of an American football.
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (3rd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
- A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 12 feet across at its opening and 4 feet deep at its center, where should the receiver be placed?arrow_forwardFind the end points of the minor and major axis for the graph of the ellipse(x−2)^2/25+(y−1)^2/36=1Maximum point on the major axis: Minimum point on the major axis: Maximum point on the minor axis: Minimum point on the minor axis: Maximum focal point: Minimum focal point:arrow_forwardMr. Yang's rugby team is facing the fighting bees next week. For the equation (x^2/a^2)+(y^2/b^2)=1 find the volume of the rugby ball used in next week's match. The ball should regularly be 11 inches end to end and the center should measure 22 inches. Estimate the area by rotating an ellipse around the y axis or the x-axis and answer the questions below.arrow_forward
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning