Question

A slice of pizza whose edges form a 32degrees angle with an outer crust edge 4 inches long was found in a gym locker. What was the diameter of the original​ pizza?g

Answer 1

Answer:

The diameter was $d=\frac{45}{\pi }$ in.

Step-by-step explanation:

The arc of a circle is given by

$s=r\theta$

where

s = arc length

r = radius of the circle

θ = measure of the central angle in radians.

From the information given

s = 4 in

θ = 32º

To find the diameter of the original​ pizza, we use the formula of the diameter of a circle

$d=2r$

First, we need to convert the angle to radians

$\theta=32\º \cdot \frac{\pi}{180\º} =\frac{8\pi }{45}$

Next, solve for r from the arc formula

$r=\frac{s}{\theta} =\frac{4}{\frac{8\pi }{45}} =\frac{45}{2\pi }$

Then, we use the diameter of a circle formula

$d=2r=2(\frac{45}{2\pi })=\frac{45}{\pi }$