Question

Find the surface area of the part of the paraboloid z = x²/2+ y²/2 that lies between the cylinders x²+ y²= 8 and x²+ y²= 24.

Answer 1

To find the surface area of the part of the paraboloid that lies between the cylinders, we can use a double integral in polar coordinates.

Step-by-step explanation:

To find the surface area of the part of the paraboloid that lies between the cylinders, we need to find the area of the paraboloid within the region enclosed by the two cylinders. The surface area can be found using a double integral in polar coordinates.

1. First, convert the inequalities of the cylinders to polar coordinates.
2. Set up the double integral for the surface area using polar coordinates.
3. Evaluate the double integral to find the surface area.

Using these steps, you can calculate the surface area of the part of the paraboloid.