Question

9. A sector of a circle has central angle

Answer 1

Answer:

Step-by-step explanation:

Begin with the formula for the area of a sector:

$A=\frac{\theta}{2\pi}*\pi r^2$ and we are given everything except the radius, r. Filling in what we know:

$\frac{49\pi}{8}=\frac{\frac{\pi}{4} }{2\pi}*\pi r^2$ and then start the simplification process. I began by dealing with the fraction over a fraction thing, which simplifies the equation to:

$\frac{49\pi}{8}=\frac{1}{8}\pi r^2$ then isolate the r-squared:

$\frac{8(49\pi)}{8\pi}=r^2$. Canceling out the π's and the 8's leaves us with simply

r² = 49 so

r = 7