Question

How can you represent the top hemisphere of a sphere using an inequality?

a) x² + y² + z² ≤ r²
b) x² + y² + z² ≥ r²
c) x² + y² ≤ r²
d) x² + y² ≥ r²

Answer 1

The top hemisphere of a sphere can be represented using the inequality x² + y² ≥ r².

Step-by-step explanation:

The correct representation of the top hemisphere of a sphere using an inequality is option d) x² + y² ≥ r².

In this inequality, x² + y² represents the equation of a circle with radius r. Any point (x, y) within or on the circle satisfies the inequality.

Since we want to represent the top hemisphere, we need all points above the circle, which is represented by the inequality symbol '≥'.