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September 4, 2015

Homework Help: Calc 3

Posted by joe on Monday, December 7, 2009 at 9:41am.

The actual span of the base of the dome is 143 feet.
1) Use cylindrical coordinates to write the surface of the dome as a function of the
distance from the center of the base; that is find z = f (r) .
2) Use your function to find the height of the dome; that is what is f (0) ?
3) Find the volume of the inside of the dome.
4) Assume the density is one, that is
P(r,"theta",z)=1 :
a. Find the moment around the x-y plane.
b. Use 3) and a) above to find the center of mass for the dome.
5) The density of the sides decreases as the dome gets higher. Assume that the
density is P(r,"theta",z)=k∗(f(0)−z) where k is a constant.
a. Find the mass of the dome.
b. Find the moment around the x-y plane.
c. Find the center of mass of the dome.

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