Question

The sector shows the area of a lawn that will be watered by a sprinkler. What is the area, rounded by the nearest tenth? Use 3.14 for pi.

Answer 1

The sector shows the area of a lawn that will be watered by a sprinkler. What is the area, rounded by the nearest tenth? Use 3.14 for pi.

Answer 2

I learned this a few years ago, let me do some sniffing

Answer 3

Which degree measure corresponds to a full rotation?

Answer 4

Or jim can help you out ;)

Answer 5

Wait, 360? @jim_thompson5910

Answer 6

yes 360 degrees

Answer 7

what fraction of 360 is 30?

Answer 8

12

Answer 9

more like 1/12 actually

Answer 10

But how could I calculate the area from here?

Answer 11

since 30/360 = 1/12

Answer 12

so 1/12 of the circumference is equal to 10 ft, which is the arc length

Answer 13

what is the circumference of this whole circle?

Answer 14

@jim_thompson5910 isn't the circumference 10x12?

Answer 15

120 yep

Answer 16

now you know the circumference

Answer 17

how can you use this to find the radius of the circle?

Answer 18

Yes but the area formula does not involve the circumference, so how do we calculate the radius from there?

Answer 19

what is the circumference formula?

Answer 20

pi*d

Answer 21

and d = 2r

Answer 22

yes

Answer 23

so C = pi*2r or C = 2*pi*r

Answer 24

you can use C = 120 to find r

Answer 25

but I don't know how to calculate the radius

Answer 26

plug in C = 120 and solve for r

Answer 27

I finished the process and I found the answer!! 95

Thank you so much for guiding me through the steps.