Question

I need help with my work ASAP

Answer 1

Explanation:

The area for the sector of a circle is

`A_s=(theta)/(360)*\pi r^2` 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:

`64\pi =(90)/(360)*\pi r^2`

Let's get that solved for r-squared first:

`(360(64\pi ))/(90\pi ) =r^2`

Doing all the math on that gives us:

`256=r^2`

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.