Question

What do level curves of a sphere look like?

Answer 1

In this problem we have given that the level curve of looks like . So in general we know that the equation of sphere is generally given by

Where r is the radius of the sphere

For the leveling of the curve we must plot it in XY plane so we take the equation involving x and y and we vary the value of z so what we get here is the equation of circle with varying the area since z is varying. So the level of the curve of sphere will look like as sphere with changing shape(area) increasing as z is increased for a certain value and then decreased after the certain point.

The equation of the circle (from sphere in x and y ) is

With varying z

So the level of curve of sphere will look like as circle.