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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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
which should come out to ~41
That is what I had put on my homework and he counted it wrong. I think that is for length, not area.
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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
which should be roughly 125 square centimetres
where did the five come from?
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
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
if that helps you picture it
ok, I don't know what i did but i did not get 301.44
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