Question

Use polar coordinates to find the volume of the given solid.......Please explain how

Answer 1

Bounded by the paraboloids \[z=7x^2+7y^2 and z=8-x^2-y^2\]

Answer 2

@dumbcow

Answer 3

here is how i would do this problem (sorry not polar coord)
they intersect at circle x^2 + y^2 = 1 when z = 7
separate volume into lower paraboloid and upper parabaloid
each can be found by summing up the areas of the cross-sectional circles
lower:
\[x^{2} +y^{2} = \frac{z}{7}\]
upper:
\[x^{2} + y^{2} = 8-z\]
\[V = \pi \int\limits_0^7\frac{z}{7} dz + \pi \int\limits_7^8 (8-z) dz\]

Answer 4

@chrisplusian