Stuck on question relating shaded areas of congruent shapes to percentages

[Simonsky]

I'm sure the answer to this question is simple but I seem to have 'brain freeze' every time I look at it!

The question is No. 8 on the attachment:

It seems to me that you need to find out the percentage of the shaded area of A obtuse the obtuse angle lines but I can't get there-any pointers gratefully received!

 

[Dr.Peterson]

I'm sure the answer to this question is simple but I seem to have 'brain freeze' every time I look at it!

The question is No. 8 on the attachment:

It seems to me that you need to find out the percentage of the shaded area of A obtuse the obtuse angle lines but I can't get there-any pointers gratefully received!

I think you have the main idea, though I don't know what "obtuse the obtuse angle lines" means (typo?).

What fraction of the circle is contained between the two radii in C?

Will the same be true of any circle with the same center? (You might want to think about similar figures, though that is not needed.)

Then, what fraction of the inner circle will be shaded? And what area is that?

 

[Simonsky]

I think you have the main idea, though I don't know what "obtuse the obtuse angle lines" means (typo?).

What fraction of the circle is contained between the two radii in C?

Will the same be true of any circle with the same center? (You might want to think about similar figures, though that is not needed.)

Then, what fraction of the inner circle will be shaded? And what area is that?

Thanks for the nudge, Dr. Peterson-let me see:

Well, the inner circle (as in A) is 2/3 shaded and C is 3/5 shaded and the outer ring will be 1/3 of the area. The unshaded part of C is therefor 2/5- still not sure how to use this inormation!

 

[Dr.Peterson]

Thanks for the nudge, Dr. Peterson-let me see:

Well, the inner circle (as in A) is 2/3 shaded and C is 3/5 shaded and the outer ring will be 1/3 of the area. The unshaded part of C is therefor 2/5- still not sure how to use this information!

I don't see a need to talk about the unshaded parts.

But it looks like you are misinterpreting the question.

A tells you that the inner circle is 2/3 of the whole.

C tells you that the sector is 3/5 of the whole (and the same will be true of any circle).

What fraction of the whole is the sector of the inner circle?

 

[Simonsky]

I don't see a need to talk about the unshaded parts.

But it looks like you are misinterpreting the question.

A tells you that the inner circle is 2/3 of the whole.

C tells you that the sector is 3/5 of the whole (and the same will be true of any circle).

What fraction of the whole is the sector of the inner circle?

Well, if C is 3/5 (60%) then B's inner circle is also 3/5 of the inner circle which is then 3/5 x 2/3 of the whole circle which is 6/15 = 2/5 which is correct after checking answer at back of book. Phew-I really tortured that question which should have been easy!