Some concepts regarding area that I need help understanding


by fwb
Tags: concepts
fwb
fwb is offline
#1
Sep26-06, 09:59 PM
P: 3
Most 3d volume formulas look similar to their corresponding 2d area formulas for a particular shape. How does calculus, specifically integration, relate the two sets of formulas?

For example: how is the formula of a cone derived from the formula of a circle?
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
mathman
mathman is offline
#2
Sep27-06, 02:45 PM
Sci Advisor
P: 5,942
One method: 3d coordinate system - put cone point at origin and cone axis along positive x axis. Let h be height of cone and R=radius of base. Let k=R/h. The radius of the cone circle defined by a plane at point x perpendicular to the x axis is given by r=kx. The differential of volume at a point x is then pi*r2dx. Integrate from 0 to h and the volume will be pi*k2h3/3=pi*R2h/3.

There may be neater ways, but you can see the point.


Register to reply

Related Discussions
Understanding mechanical concepts Classical Physics 52
Understanding concepts General Discussion 5
Tips 4 Understanding concepts Calculus 5
Momentum Concepts [Checking my Understanding] Introductory Physics Homework 2
Do formulas prevent students from understanding concepts? Academic Guidance 36