Ying Yang symbol problem

[17rkearns]

I've been working on geometry in math, when this question came up I had no idea what to do. The only thing that I've been able to figure out is that the radius has something to do with this problem because it's the only measurement shown. I don't know if you can see the picture very well, but it's a ying yang symbol. The shaded side is labeled a, and the blank side is labeled b. The radius which goes through the b section of the picture is 1.5 meters. I have to find the measurement of the curved line between sections a and b to complete the problem. As I said before, the only thing that I have an idea about is the fact that the radius has to have some sort of relation to the problem. Thanks!

 

[srmichael]

I've been working on geometry in math, when this question came up I had no idea what to do. The only thing that I've been able to figure out is that the radius has something to do with this problem because it's the only measurement shown. I don't know if you can see the picture very well, but it's a ying yang symbol. The shaded side is labeled a, and the blank side is labeled b. The radius which goes through the b section of the picture is 1.5 meters. I have to find the measurement of the curved line between sections a and b to complete the problem. As I said before, the only thing that I have an idea about is the fact that the radius has to have some sort of relation to the problem. Thanks!
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When you say "measurement" I assume you mean length.

Take another look at the curved line. Do you see how this curved line can be made into another curved line? Maybe one that would allow you to use the radius given to you????

 

[17rkearns]

When you say "measurement" I assume you mean length.

Take another look at the curved line. Do you see how this curved line can be made into another curved line?

Maybe one that would allow you to use the radius given to you????

Yes I do mean length sorry about that. Do I just take the radius and multiply it twice because it's going across the curved lines? Also, I have to figure out the area of shaded figure A, How do I do that??? Do both of these problems involve semi circles??

 

[srmichael]

Yes I do mean length sorry about that. Do I just take the radius and multiply it twice because it's going across the curved lines? Also, I have to figure out the area of shaded figure A, How do I do that??? Do both of these problems involve semi circles??

Not quite. The curved line from Point A to the center of the big circle and from Point B to the center of the big circle makes a smaller circle with diameter 1.5 meters? Do you see that. Then you can find the length (circumference).

As far as the shaded region goes, do you see that the shaded region and the unshaded region are perfectly symmetrical? What does that tell you about the area of the shaded region?

 

[17rkearns]

When you say "measurement" I assume you mean length.

Take another look at the curved line. Do you see how this curved line can be made into another curved line? Maybe one that would allow you to use the radius given to you????

Not quite. The curved line from Point A to the origin and from Point B to the origin makes a circle with diameter 1.5 meters? Do you see that. Then you can find the length (circumference).

As far as the shaded region goes, do you see that the shaded region and the unshaded region are perfectly symmetrical? What does that tell you about the area of the shaded region?

What's the origin??? I do see that if you flip one curved line that it creates a whole circle if that's what you mean.
Ummmm It means that its 1/2 of the whole area of the circle????

 

[srmichael]

What's the origin??? I do see that if you flip one curved line that it creates a whole circle if that's what you mean.
Ummmm It means that its 1/2 of the whole area of the circle????

I've been working too hard. I meant center of the big circle, not origin. But yes, you see that it creates a smaller whole circle.

And you are correct on the area of the shaded region too!