Multiple Integrals Word Problem

W

whizvish

New member
Joined
Oct 21, 2007
Messages
8
"A region in space, when viewed from 3 different views, looks like a circle, a square and a triangle. Describe this object
with either figure or with words. Use multiple integration to determine its volume, in terms of diameter a"

So I'm having difficulty getting this problem started and doing it. I'm lost, help would be greatly appreciated. :D
 
I don't know how to "describe" it, without just giving you the answer. And I sure can't draw! :wink:

So.... Try grabbing some modelling clay or Silly Putty or something similar, and working with the shapes. For instance, if you make a cylinder, this will look like a circle, when viewed from the end. What does it look like from the side? Is there a way to turn that side view into a square? And so forth. :idea:

Have fun! :D

Eliz.
 
hmm interesting.. I'll give that a try. How would I set up the multiple integration to find the volume...
Also, is there another way to figure out the shape? Something more math orientated. =D thanks.
 
Hello, whizvish!

A region in space, when viewed from 3 different views, looks like a circle, a square and a triangle.
Describe this object with either figure or with words.
Use multiple integration to determine its volume, in terms of diameter a.
Click to expand...

This is a classic (very old) problem.

Consider a right circular cylinder with diameter \(\displaystyle a\) and height \(\displaystyle a\).
Stand it on one of its circular bases.

From the top, it looks like a circle.
From the side, it looks like a square.
Code: 
      *---------------*
      |               |
      |               |
      |               |
      |               | a
      |               |
      |               |
      |               |
      *---------------*
              a


Make two diagonal slices as shown below.
Code: 
      * - - - * - - - * 
      :      / \      :
      :     /   \     :
      :    /     \    :
      :   /       \   : a
      :  /         \  :
      : /           \ :
      :/             \:
      *---------------*
              a
The resulting solid has a circular shape when seen from above,
. . a square shape when seen from the right (or left),
. . and a triangular shape when seen from the front.


Now you can visualize this solid . . . or not.

 
You must log in or register to reply here.
Top