March 29, 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.

Answer this Question

First Name:
School Subject:

Related Questions

Science: Physics - A spherical metal dome of radius 15 cm is electrically ...
AP Calc - The picture to the right shows the Ben Franklin Bridge which stretches...
math - the dome over a town hall has a parabolic shape. the dome measures 48 m ...
AP Calculus AB - Please Help! Thank you! An observatory is to be in the form of ...
Calculus - Find the force on a hollow dome that is 1000 feet in diameter, that ...
Math - Charlie is making a toy silo for his children. The silos height is three ...
Physics(IMPORTANT) - A small object of mass m= 90 kg slides down a spherical ...
physics - A particle of mass m is released from rest at the top of a spherical ...
Math - For a history project, Marcus built a replica of the Texas State Capitol ...
physics - The dome of a Van de Graaff generator has a diameter of 32.0 cm and is...