Question

decide if this biconditional statement is true or false. the area of a circle is 9π if and only if its radius is 3. false true

Explanation:

Step1: Analyze forward implication

If radius \(r = 3\), area \(A=\pi r^{2}=\pi\times3^{2}=9\pi\).

Step2: Analyze reverse implication

If \(A = 9\pi\), then \(\pi r^{2}=9\pi\). Divide both sides by \(\pi\): \(r^{2}=9\), so \(r = 3\) (radius is non - negative).

Answer:

True