Manuel wants to build a model of a superhero's famous shield. He decides to cut a circular shape out of cardboard. Manuel knows that the outer ring of the shield is colored yellow. The next ring is white. The third ring in is also yellow. The center is white with a green key. The radius of the entire shield is 12 inches; however, Manuel wants to know how much yellow paint he will need so he does some measurements as shown in the diagram below. He measures the radius of the inner circle as 4.5 inches. He measures the radius to the second circle as 7 inches. The radius to the third circle as 9.5 inches. What is the area of the space Manuel will paint yellow? Use 3.14 for pi

B : 259.18in^3

Step-by-step explanation:

find the area of all the circles you have to use the formula A=πr2 and these are the sizes

smallest white : A≈63.62in

yellow 2nd circle: A≈153.94in

3rd circle white: A≈283.53in

largest yellow circle: A≈452.39in

first you have to start with the smallest circle which the area is 63.62 then you go to the 2nd circle which is yellow which the area is 153.94 since you are trying to find only the area of yellow you have to subtract 63.62 from 153.94 which you get 90.32 then you have to go to the 3rd circle which then you have to subtract the 90.32 from 283.53 which comes out to be 193.21 then you finish with the last circle which the area is 452.39 then you have to subtract the last 193.21 which comes out to be 259.18in

the reason you subtract every time you went to the bigger circle because that number was the opposite color if you had 2 yellows in a row you would have to add them just as an example.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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