Answer:
Explanation:
The area for the sector of a circle is
where theta is the measure of the central angle. We have some given values to fill in:
Area is 64π and the central angle is 90°, so all we have left to find is the radius. Filling into the equation:

Let's get that solved for r-squared first:
Doing all the math on that gives us:

Take the square root of both sides and get that r = ±16. BUT we know that lengths cannot be negative, so we disregard the -16 and say that the radius is 16 inches.