Question

Describe in words the region of R3 reperesented by the equations or inequalities y2+z2=16

Answer 1

It represents an infinite cylinder of radius 4.

Explanation:

The first thing to notice is that

`y^2+z^2=4^2`

represents a circle of radius 4, with its center in the origin of a plane yz, of cartesians coordinates.

Starting from here, we have to put the coordinate x, for all values of x, to complete the space R³. This will enlarge this circle we had on the plane, to infinity (positive and negative on the x-axis).

Finally, we have that this region is a cylinder of radius 4, with center in y=0 and z=0, and of infinite length in the x coordinates.