Finding the Center of Mass of a Hemisphere

[ritwik06]

Homework Statement

Center of Mass of a hemisphere

http://www.goiit.com/templates/default/images/chapters/center_mass/image064.gif
http://www.goiit.com/templates/default/images/chapters/center_mass/image068.gif
Why is volume of elemental disc = Rd\theta (cos \theta) (\pi R^{2}cos^{2} \theta) and not

Rd\theta (\pi R^{2}cos^{2}\theta)?

 

[gabbagabbahey]

Because the arc length is measured from the \theta=0 plane (yz plane) to the plane rotated through an angle d\theta, So the radius of the arc is the projection of R onto the \theta=0 plane which is Rcos(\theta) and so the arc length is Rcos(\theta)d\theta.

 

[ritwik06]

Because the arc length is measured from the \theta=0 plane (yz plane) to the plane rotated through an angle d\theta, So the radius of the arc is the projection of R onto the \theta=0 plane which is Rcos(\theta) and so the arc length is Rcos(\theta)d\theta.

I don't get it. Could you please take some of ur precious time out, just to draw a very rough sketch in paint? Please!