Finding the volume of a cone.doc - Finding the volume of a cone Step 1 – recapping a 2-D method Use the trapezium rule with strips of height h = 1 cm

Finding the volume of a cone.doc - Finding the volume of a...

This preview shows page 1 - 3 out of 3 pages.

Finding the volume of a cone Step 1 – recapping a 2-D method Use the trapezium rule with strips of height h = 1 cm to estimate the area of this triangle: Improve your estimate by using strips of height h = 0.5 cm and then h = 0.2 cm. What is the actual area of the triangle? What can you say about your successive estimates? Step 2 – extending the method to 3-D The triangle has now been rotated around the x axis to form a cone. What 3-D shape are your ‘strips’? It may help to visualise a child’s toy with rings of decreasing size on a peg. Use discs of height δx = 1 cm to estimate the volume of the cone. Repeat for discs of height δx = 0.5 cm and δx = 0.2 cm. Use a spreadsheet to predict the actual volume of the cone. Is this what you expected? Repeat for a cone with a different height and base radius. 10 5 x y 10 5 x y
Image of page 1
Step 3 – generalising Find the volume of the disc which starts x units from the vertex and has height δx, and of the next disc.
Image of page 2
Image of page 3

You've reached the end of your free preview.

Want to read all 3 pages?

  • Fall '17
  • William Heywood

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes
A+ icon
Ask Expert Tutors