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    Finding the volume of a rugby ball (or American football) | IB Maths Resources from Intermathematics

    if you’re a teacher, also visit my new site: intermathematics.com for over 2000 pages of ib maths teaching resource pdfs.

    Reading: What is the volume of a football

    find the volume of a rugby ball (elongated spheroid)

    With the rugby world cup currently underway, I thought I’d try to calculate the volume of a rugby ball using some calculations. this method works similarly for American football and Australian rules football. The approach is to consider the rugby ball as an ellipse rotated 360 degrees about the x-axis to create a volume of revolution. we can find the equation of an ellipse centered at (0,0) simply by looking at the x and y intercepts. an ellipse with y-intercept (0,b) and x-intercept (a,0) will have the equation:

    so for our rugby ball with a horizontal (vertex) “radius” of 14.2 cm and a vertical (co-vertex) “radius” of 8.67 cm, you will have the equation:

    We can see that when we plot this ellipse we get an equation that closely resembles the shape of our rugby ball:

    so now we can find the volume of revolution using the following formula:

    but we can simplify things by starting the rotation at x = 0 to find half the volume, before doubling our answer. therefore:

    reordering our equation of the ellipse formula we get:

    therefore we have the following integration:

    See also: 2021 SheBelieves Cup: USA vs. Brazil – Match History & Preview | Five Things to Know

    so our rugby ball has a volume of around 4.5 litres. we can compare this to the volume of a football (soccer ball), which has a radius of around 10.5 cm, hence a volume of around 4800 cubic centimeters.

    We can find the overall volume of any rugby ball (mathematically defined as an elongated spheroid) by the following generalization:

    We can see that this is closely related to the formula for the volume of a sphere, which makes sense since the elongated spheroid behaves like a sphere deformed on its axes. our elongated spheroid has “radii” b, b, and a; therefore, r cubed in the sphere formula becomes b squared a.

    elongated spheroids in nature

    The image above [wiki image nasa] is of the Crab Nebula, a distant supernova remnant about 6500 light-years away. the shape of the crab nebula is described as an elongated spheroid.

    essential resources for ib students:

    See also: The 50 best college football programs over 150 years | Pro Football Hall of Fame Official Site

    1) review village

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    revision village has been created to help ib students with revision of topics both during the course and for year 12 school exams and year 13 final exams. I would highly recommend students to use it As a resource during the course (not just for the final review in y13!) there are specific resources for hl and sl students for both analysis and applications.

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    There is a comprehensive question bank that takes you through a breakdown of each major subject area (eg Algebra, Calculus, etc.) and then provides a large bank of graded questions. what I like about this is that they give you a difficulty rating as well as an outline of marks and also a worked video tutorial. really useful!

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    The practice exams section takes you to a wealth of ready-to-use quizzes, exams, and job previews. all of these have solutions that work and allow you to zero in on specific topics or start a general review. this also has some great challenging questions for those students looking for 6s and 7s.

    essential resources for ib teachers

    1) intermathematics.com

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    If you’re a teacher, check out my new site too. this has been specifically designed for math teachers in international schools. content now includes over 2000 pages of pdf content for the entire sl and hl analytics syllabus and also the sl applications syllabus. some of the content includes:

    1. original pdf worksheets (with full solutions) designed to cover all syllabus topics. these are great homework sheets or class worksheets, and are designed to last between 40 minutes and 1 hour.
    2. original investigations of article 3 (with complete solutions) for develop technical investigations and support for both the exploration and the Test 3 exam.
    3. over 150 pages of coursework guides to introduce students to the essentials to get an A on your exploration coursework.
    4. a host of enrichment activities such as scavenger hunts, quizzes, investigations, desmo explorations, online programming python and more, to engage ib students in the course.

    there is also much more. I think this could save teachers over 200 hours of prep time to teach an ib maths course, so it’s worth exploring!

    essential resources for ib teachers and students

    1) navigation guides and document resources 3

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    I’ve put together a super 168 page exploration guide to talk to students and teachers about all aspects of producing a great coursework presentation. students always make the same mistakes when doing their coursework – get in-depth insights from an ib moderator! i have also made paper 3 packs for hl analysis and also apps for students to help them prepare for their paper 3 exams. the scan guides can be downloaded here and the 3 questions in the paper can be can download here.

    See also: Live Updates: Virginia Tech Defeats Virginia 29-24 – Sports Illustrated Virginia Cavaliers News, Analysis and More

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