Question

d = 20 ft
what is the area of the slice of pie that was cut, rounded to the nearest hundredth?
22.08 ft²
13.19 ft²
33.14 ft²
28.97 ft²

Explanation:

Step1: Find the radius

Given diameter $d = 20$ ft, radius $r=\frac{d}{2}=\frac{20}{2}=10$ ft.

Step2: Use the sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta = 38^{\circ}$ and $r = 10$ ft. Substitute the values: $A=\frac{38^{\circ}}{360^{\circ}}\times\pi\times(10)^{2}$.

Step3: Calculate the area

$A=\frac{38}{360}\times\pi\times100=\frac{3800\pi}{360}=\frac{95\pi}{9}\approx\frac{95\times3.14159}{9}\approx33.14$ ft².

Answer:

33.14 ft²