- #1

cronxeh

Gold Member

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Problem: A particular spherical cloud of gas of radius 3 km is more dense at

the center than towards the edge. The density, D, of the gas at a distance p km

from the center is given by [tex]D(p) = 9 - p^2[/tex]. Write an integral representing the total mass of the cloud of gas, and evaluate it.

Solution: density = mass/area. The spherical cloud's area is 9pi/2

mass =9/2 pi (9-p^2).

So mass = [tex]\frac{9pi}{2} \int_{0}^{pi} \int_{0}^{3} (9-r^2) \ r \ dr \ dtheta [/tex]

Is this correct?