anonymous
  • anonymous
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
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
total area of the circle is \(\pi r^2\) which in your case is \(\pi\times 10^2=100\pi\)
anonymous
  • anonymous
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
anonymous
  • anonymous
the entire circle has \(360^\circ\) to find your portion, compute \[\frac{4}{10}\times 360\] or \[.4\times 360\]

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anonymous
  • anonymous
It's 144. But why not multiply it by 180 though?
anonymous
  • anonymous
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
anonymous
  • anonymous
\[\frac{40\pi}{100\pi}=\frac{x}{360}\]
anonymous
  • anonymous
Alright I understand
anonymous
  • anonymous
k good more?
anonymous
  • anonymous
Yeah
anonymous
  • anonymous
k lets knock em ouit

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