- #1
cronxeh
Gold Member
- 1,007
- 11
I really shouldn't be stuck on those problems but for whatever reason i can't solve them
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?
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?