Volume of Triangle Rotated Around Its Base: Shells & Cylinders

[youxcrushxme]

I'm having trouble on this problem -

Find the volume of the object created by rotating an equilateral triangle around its base. Solve using both shells and cylinders.

Any help would be appreciated :)

 

[daysyworld]

Firstly you have to determine the radius of the circunference who contains the triangle. ( see the graphic below)

- triangle is an equilateral triangle, because that the angles are 180/3= 60º

If we draw the radius we have half angle ; 60/ 2 = 30 º

Whe aply trigonometry :

Cos 30 = (side/2)/ Radius --> Here you have only one unknown (radius)

Now, yo have by rotation generated circunference Radius, and the volume of the piece will be :

V = Pi*(R)^2*H

 

[mjsd]

mmm... where is the axis of rotation that creates the volume?