Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find volume of object if cross-sections are known

  1. Mar 4, 2005 #1
    The base of a certain solid is an equilateral triangle with altitude 14. Cross-sections perpendicular to the altitude are semicircles. Find the volume of the solid, using the formula [tex]V= \int_a^{b} A(x)dx[/tex]

    applied to the picture shown attached to this post (click for a better view), with the left vertex of the triangle at the origin and the given altitude along the -axis.

    i figure a= 0 and b = 14 and i will be plugging it into the formula pi*r^2 right?

    the problem i'm having is finding the cross-section. can someone lend me a hand?

    Attached Files:

  2. jcsd
  3. Mar 4, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    You'll be integrating from x=0 to x=14 right?

    First, find the length of one side of the equilateral, let's call it 2R.

    It's clear at x=0, the radius is zero and at x=14 the radius is R, and the radius varies linearly with x. So set up an equation for the radius in terms of x.
    then you can find A(x) and integrate.
  4. Mar 4, 2005 #3
    Think of a volume of revolution formed by a general line y = mx. What sort of shape does this yield and how is it related to the shape you are given?

    Thinking about this will also provide a good check as to whether your answer is correct as there is a nice formula for its volume.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook