Respuesta :
Answer:
The diameter was [tex]d=\frac{45}{\pi }[/tex] in.
Step-by-step explanation:
The arc of a circle is given by
[tex]s=r\theta[/tex]
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
[tex]d=2r[/tex]
First, we need to convert the angle to radians
[tex]\theta=32\º \cdot \frac{\pi}{180\º} =\frac{8\pi }{45}[/tex]
Next, solve for r from the arc formula
[tex]r=\frac{s}{\theta} =\frac{4}{\frac{8\pi }{45}} =\frac{45}{2\pi }[/tex]
Then, we use the diameter of a circle formula
[tex]d=2r=2(\frac{45}{2\pi })=\frac{45}{\pi }[/tex]
