Question

A pecan pie is being served for dessert. One piece of pie has an arc length of 7.85 in. It has been cut into 8 equal pieces. What is the radius of the pecan pie? (Round to the nearest whole number)

Answer 1

Answer: 10 inches.

Step-by-step explanation:

Since the pecan pie is a circle, you can use this formula:

$arc\ length=r\theta$

Where "r" is the radius and $\theta$ is the central angle of the arc in radians.

If the pecan pie has been cut into 8 equal pieces then the central angle is:

$\theta=\frac{2\pi}{8}\\\\\theta={\frac{\pi}{4}$

Now you know the arc length and the central angle, then, you can solve for "r" from  $arc\ length=r\theta$:

 $\frac{arc\ length}{\theta} =r$

Substituting values, you get that the radius of the pecan pie rounded to the nearest whole number is:

$r=\frac{7.85in}{\frac{\pi}{4}}\\\\r=10in$