Answer:
Step-by-step explanation:
The area for the sector of a circle is
[tex]A_s=\frac{theta}{360}*\pi r^2[/tex] 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:
[tex]64\pi =\frac{90}{360}*\pi r^2[/tex]
Let's get that solved for r-squared first:
[tex]\frac{360(64\pi )}{90\pi } =r^2[/tex]
Doing all the math on that gives us:
[tex]256=r^2[/tex]
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.
