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anonymous

  • one year ago

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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  1. anonymous
    • one year ago
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    total area of the circle is \(\pi r^2\) which in your case is \(\pi\times 10^2=100\pi\)

  2. anonymous
    • one year ago
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    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

  3. anonymous
    • one year ago
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    the entire circle has \(360^\circ\) to find your portion, compute \[\frac{4}{10}\times 360\] or \[.4\times 360\]

  4. anonymous
    • one year ago
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    It's 144. But why not multiply it by 180 though?

  5. anonymous
    • one year ago
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    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

  6. anonymous
    • one year ago
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    \[\frac{40\pi}{100\pi}=\frac{x}{360}\]

  7. anonymous
    • one year ago
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    Alright I understand

  8. anonymous
    • one year ago
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    k good more?

  9. anonymous
    • one year ago
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    Yeah

  10. anonymous
    • one year ago
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    k lets knock em ouit

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