Question

Find the volume of the solid enclosed by the paraboloids z=25(x2+y2) and z=8?25(x2+y2).

Answer 1

The paraboloids do not intersect and there is no solid enclosed by them.

Step-by-step explanation:

To find the volume of the solid enclosed by the paraboloids, we need to set up a double integral in cylindrical coordinates. The paraboloids are symmetric about the z-axis, so we can focus on the region where z ≥ 0. We can rewrite the paraboloids as:

z = 25(r^2)

z = 8+25(r^2)

Setting them equal to each other, we get:

25(r^2) = 8+25(r^2)

Simplifying, we get:

0 = 8

Since this equation has no solution, it means that the paraboloids do not intersect and there is no solid enclosed by them.