Question

Find the measure of an arc given that the shaded region has an area of 45.55 square centimeters if the radius is 6?

Answer 1

What is area of arc?

Answer 2

that shows the diagram

Answer 3

arc is the same as the angle given

Answer 4

there is no angle

Answer 5

Actually, lets start with the area of the circle

Answer 6

whats 45.55

Answer 7

the area of shaded region

Answer 8

do you find area of circle and put 45.55 over area as a proportion to x/360? to find arc angle?

Answer 9

Yes

Answer 10

Then you have x/360 and times this by circumference to get arc length

Answer 11

is it 144.99?

Answer 12

Area of circle: 36pi
sector area/circle area: 45.55/36pi ~ 0.403

Circumference: 12pi
Arc length: 12pi*45.55/36pi = 45.55/3 ~15.18

Answer 13

area of full circle is :
\[\pi r ^{2}\]
the proportion of a sector to the full area is same as the angle of the sector to the full angle:
\[45.55/\pi*6 ^{2}=x/2 \pi\]
from here :
\[x=(45.55*2)/36\]

Answer 14

notice that x is in radians. To get the answer in centimiters multiply it by 6