It seems to me (one man's opinion), that your math teacher tried to incorporate two different concepts into one problem, and did not account for a logical inconsistency. The teacher was trying to use the well known "area of a circle" formula, to construct a problem in which you had to solve a quadratic equation.
However, I believe that the teacher forgot one important difference between the algebra of quadratics and the solid constructs of geometric figures: a quadratic equation can be solved with a negative answer without any logical difficulties, yet a PHYSICAL construct like a "radius" or any piece of a geometric figure can not have a "negative size." We can sidestep this inconsistency by assuming the teacher didn't notice that the circle would have radius -3, by just blindly plugging in the numbers and hoping that we are conforming with the teacher's intent: -3 squared = 9, so the small circle has an area of 9pi units squared. Alternatively, we can think of it as when the radius of the circle shrinks past zero into "negative territory" that the circle begins to grow again: i.e. that a circle with "negative" radius is the same as the circle of one with the absolute value
of that radius.
however, these arguments are designed to escape a fundamental flaw in the construction of the problem, and if we're being stringent with our application of algebra to a geometry problem, this figure could not exist. it should be a basic necessity in constructing a problem that the radius (or the length of any other physical structure within the graph) be greater than or equal to zero. because an object cannot have negative size. it is logically inconsistent with reality.
that's not to say that concepts like "negative area", "negative volume," "directional vectors being akin to negative distance," etc. aren't entirely useful - in fact they have vast
application in more conceptual areas of mathematics like calculus, differential equations, and beyond. but for the purposes of this problem, i'd bet the teacher just didn't notice the flaw in their problem's construction, and would probably ask you to do the same.