Question

A giant pie is created in an attempt to break a world record for baking. The pie is shown below: What is the area of the slice of pie that was cut, rounded to the nearest hundredth?
78.13 ft
82.43 ft
86.31 ft
91.98 ft

Answer 1

if the "d"iameter of the pie is 30, then its radius must be half that, or 15.

$\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=15\\ \theta =42 \end{cases}\implies \begin{array}{llll} A=\cfrac{(42)\pi (15)^2}{360}\implies A=\cfrac{105\pi }{4} \\\\\\ \stackrel{using~\pi =3.14}{A\approx 82.43} \end{array}$