Posted by Jack Eaton on October 03, 2002 at 12:57:20:
In Reply to: calculus posted by jeff on October 03, 2002 at 03:12:26:
: A spherical tank having a radius of 12' caontains some liquid.
: a) How much liquid (in cubic Feet) would there be in this tank if the depth of the liquid is 4 feet?
:First, derive the formula for the volume in question. Using the disk method of Solids of Revolution, you have the integral I pi*(144-y^2)dy integrated over the interval -12 to -12+h, where h is the depth of the liquid. Carry out this integration and get
: V(h)=12*pi*h^2-(1/3)*pi*h^3 and
: V(4)=536 cu.ft.
: b) How deep would this liquid be (find its depth) if the tank contained 136(pie)/3 cubic feet of liquid?
:If you set V(h)=136*pi/3 and solve for h, you find that V(h=2)=136*pi/3.
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