3.2k views
2 votes
Find the volume of the solid enclosed by the paraboloids z=25(x2+y2) and z=8?25(x2+y2).

User DeFreitas
by
8.1k points

1 Answer

4 votes

Final answer:

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.

User Andre Lee
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories