In a circle of radius 10 cm, a sector has an area of 40pi sq. cm. What is the degree measure of the arc of the sector? a) 72° b) 144° c) 180°

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In a circle of radius 10 cm, a sector has an area of 40pi sq. cm. What is the degree measure of the arc of the sector? a) 72° b) 144° c) 180°

Mathematics
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total area of the circle is \(\pi r^2\) which in your case is \(\pi\times 10^2=100\pi\)
the sector has area \(40\pi\) and \(\frac{40\pi}{100\pi}=\frac{4}{10}\) in other words the area of the sector is four tenths of the total area
the entire circle has \(360^\circ\) to find your portion, compute \[\frac{4}{10}\times 360\] or \[.4\times 360\]

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Other answers:

It's 144. But why not multiply it by 180 though?
this is a different knd of problem than the last one we are not converting from degrees to radians or anything just computing a ratio
\[\frac{40\pi}{100\pi}=\frac{x}{360}\]
Alright I understand
k good more?
Yeah
k lets knock em ouit

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