f(x,y,z) = 1
S is solid region bounded below by half-cone z = sqrt(x^2+y^2) and above by circular paraboloid z = 6-x^2-y^2
Find the volume of S using cylindrical coordinates.

I have a triple integral of r with:
z going from r to 6-r^2
r going from 0 to sqrt(3)
theta going from 0 to 2pi

I get 2pi[27/4-3sqrt(3)], but the answer is (32/3)pi. Please help :)

Question

f(x,y,z) = 1
S is solid region bounded below by half-cone z = sqrt(x^2+y^2) and above by circular paraboloid z = 6-x^2-y^2
Find the volume of S using cylindrical coordinates.

I have a triple integral of r with:
z going from r to 6-r^2
r going from 0 to sqrt(3)
theta going from 0 to 2pi

I get 2pi[27/4-3sqrt(3)], but the answer is (32/3)pi. Please help :)

zepdrix · Answer

Hmm where did r=sqrt3 come from? Don't the lines intersect at r=2? :o

anonymous · Answer

|dw:1351969548482:dw|