Question

decide if this biconditional statement is true or false. the circumference of a circle is 8π if and only if its radius is 4. true false

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C = 2\pi r\).

Step2: Substitute \(r = 4\) into the formula

When \(r = 4\), \(C=2\pi\times4 = 8\pi\).

Step3: Solve for \(r\) when \(C = 8\pi\)

If \(C = 8\pi\), then from \(C = 2\pi r\), we have \(8\pi=2\pi r\). Dividing both sides by \(2\pi\) gives \(r = 4\).

Answer:

True