3 years ago

360 miles in a tank o27f gas

Mathematics

1 answer:

Lana71 [14]3 years ago

8 0

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What is the angle measure of an arc bounding sector with an area of 5pie square miles?

Snowcat [4.5K]

if the diameter is 20, the its radius must be half that or 10.

$\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}$