Question

Find the part of the sphere x2 y2 z2 = 4 that lies above the cone z = √x2 y2

Answer 1

The part of the sphere that lies above the cone is the portion where x² + y² is greater than or equal to 2.

Step-by-step explanation:

To find the part of the sphere that lies above the cone, we need to determine the intersection between the sphere and the cone.

The cone equation is z = √(x² + y²), and the sphere equation is x² + y² + z² = 4.

Solving these equations simultaneously, we substitute the cone equation into the sphere equation to get x² + y² + (√(x² + y²))² = 4.

Simplifying this equation gives us x² + y² + x² + y² = 4, which simplifies further to 2x² + 2y² = 4.

Dividing both sides by 2, we get x² + y² = 2.

So, the part of the sphere that lies above the cone is the portion where x² + y² is greater than or equal to 2.