Question

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.

Answer 1

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

Answer 2

which should come out to ~41

Answer 3

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

Answer 4

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

Answer 5

which should be roughly 125 square centimetres

Answer 6

where did the five come from?

Answer 7

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

Answer 8

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

Answer 9

if that helps you picture it

Answer 10

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

Answer 11

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

Answer 12

ok, thank you. I understand.