## haleyking345 2 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.

1. funinabox

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

which should come out to ~41

3. haleyking345

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

4. funinabox

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

which should be roughly 125 square centimetres

6. haleyking345

where did the five come from?

7. funinabox

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

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

if that helps you picture it

10. haleyking345

ok, I don't know what i did but i did not get 301.44

11. funinabox

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

ok, thank you. I understand.