Circumference of circle \(=2\pi r\)
So we can write: \(2\pi r<16\pi\)
Divide both sides of the inequality by \(2\pi\) to get: \(r<8\)
In other words, the radius is less than 8

Area of circle \(=\pi r^2\)
If the radius were EQUAL to \(8\), then the area of the circle \(=\pi (8^2)=64\pi\)

Since the radius is less than 8, the area of the circle must be LESS THAN \(64\pi\)

Answer choice A is the only answer that is less than \(64\pi\)

Answer: A

Cheers,
Brent