Question

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

Explanation:

Step1: Find the radius

The diameter \(d = 20\) ft. The radius \(r=\frac{d}{2}\), so \(r = 10\) ft.

Step2: Use the sector - area formula

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle and \(r\) is the radius. Here, \(\theta = 38^{\circ}\) and \(r = 10\) ft.
Substitute the values into the formula: \(A=\frac{38}{360}\times\pi\times(10)^{2}\).
First, calculate \((10)^{2}=100\). Then \(\frac{38}{360}\times100\times\pi=\frac{3800}{360}\times\pi\).
Simplify \(\frac{3800}{360}=\frac{95}{9}\approx10.56\).
So \(A\approx10.56\times3.14 = 33.14\) (using \(\pi\approx3.14\)).

Answer:

\(33.14\space ft^{2}\)