CK12 Calculus - Single Variable

Figure7b
Solution:

Let the -axispassthroughthe apexof the pyramid,as shownin Figure(7a). At any point in the interval
the cross-sectionalarea is a square.If is the lengthof the sidesof any arbitrarysquare,then,by
similartriangles(Figure7b),

b

Sincethe cross-sectionalarea at is

Usingthe volumeformula,

V

Using -substitutionto integrate,we eventuallyget

V

Thereforethe volumeof the pyramidis , whichagreeswith the standardformula.

Volumesof Solidsof Revolution
The Methodof Disks