Question

A slice of pizza whose edges form a 42degrees angle with an outer crust edge 4 inches long was found in a gym locker. What was the diameter of the original​ pizza?

Answer 1

Answer:

10.9 inches.

Step-by-step explanation:

We have been given that a slice of pizza whose edges form a 42 degrees angle with an outer crust edge 4 inches long was found in a gym locker. We are asked to find the diameter of the original pizza.

We will use arc length formula to solve our given problem.

$s=r\theta$, where,

s = Perimeter or circumference of circle,

r = Radius,

$\theta$ = Angle in radians.

Let us convert 42 degree to radians.

$42^{\circ}\times\frac{\pi}{180^{\circ}}=\frac{7\pi}{30}$

$4=\frac{7\pi}{30}\cdot r$

$r=\frac{120}{7\pi}$

$r=5.45674090$

We know that diameter is two times radius, so

$\text{Diameter}=5.45674090\times 2$

$\text{Diameter}=10.9134818\approx 10.9$

Therefore, the diameter of the original​ pizza was approximately 10.9 inches.