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haleyking345

  • 3 years ago

What is the area of the sector of a circle if the radius is 16cm and the angle rotation is 150 degrees? I got this question wrong, so i am hoping for some help.

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  1. funinabox
    • 3 years ago
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    i think its just the radius * how much it's rotated but the degrees should be radians 150 * (pi/180) = 5pi/6 so 16 * 5pi/6 is the answer

  2. funinabox
    • 3 years ago
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    which should come out to ~41

  3. haleyking345
    • 3 years ago
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    That is what I had put on my homework and he counted it wrong. I think that is for length, not area.

  4. funinabox
    • 3 years ago
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    yes you're right one way you can do it though is to find the area of the whole circle, then find what 150/360 of it is. A = pi*r^2 A = pi*16^2 A = 301.44 but that is for 360 degrees, you want only 150. 150/360 = 5/12 so the real area is (5 * 301.44) / 12

  5. funinabox
    • 3 years ago
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    which should be roughly 125 square centimetres

  6. haleyking345
    • 3 years ago
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    where did the five come from?

  7. funinabox
    • 3 years ago
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    5 comes from the ratio 5/12, which is just a simplified 150/360 as there are 360 total degrees in a circle, and you are looking for 150 of it (little less than half the circle) so you are looking for the area of 150/360 of a circle, or 5/12 you know the area of the full circle is 301.44 so (5/12) * 301.44 should give you the smaller area

  8. funinabox
    • 3 years ago
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    basically i set up a ratio: 301.44 sq cm for 360 degrees x sq cm for 150 degrees 301.44/360 = x/150 301.44*150/360 = x 301.44*(5/12) = x x being the area

  9. funinabox
    • 3 years ago
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    if that helps you picture it

  10. haleyking345
    • 3 years ago
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    ok, I don't know what i did but i did not get 301.44

  11. funinabox
    • 3 years ago
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    301.44 is the area of the TOTAL circle you only want PART of the circle the part of the circle you are looking for, is 5/12 of the total circle. therefore, 5/12*301.44 is the answer which is about 125 square centimeters

  12. haleyking345
    • 3 years ago
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    ok, thank you. I understand.

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