Answer Checking

[MathStudent1999]

Can Someone check my answer for me? The question is : 6. Circle A has a radius of 10 units and Circle B has a radius of 5 units. The center of Circle B is on the circumference of Circle A. What is the difference between the area which is within A but not B and the area which is within B but not A. Put your answer as a multiple of Pi. My answer is 75pi.

 

[Deleted member 4993]

Can Someone check my answer for me? The question is : 6. Circle A has a radius of 10 units and Circle B has a radius of 5 units. The center of Circle B is on the circumference of Circle A. What is the difference between the area which is within A but not B and the area which is within B but not A. Put your answer as a multiple of Pi. My answer is 75pi.

$\displaystyle 75\pi$ ? How did you get that? $\displaystyle (10^2 - 5^2)\pi$? That is not correct ..... Sorry - it is correct - I was making a mistake in multiplication.

Draw the picture first.

Let common area be "C".

Let the area of the bigger circle without "C" be "B"

Let the area of the smaller circle without "C" be "S"

You need to find "B - S"

 

[MathStudent1999]

$\displaystyle 75\pi$ ? How did you get that? $\displaystyle (10^2 - 5^2)\pi$? That is not correct

Draw the picture first.

Let common area be "C".

Let the area of the bigger circle without "C" be "B"

Let the area of the smaller circle without "C" be "S"

You need to find "B - S"

No, this is what I did: Using the cosine law, I found the central angle of Circle A was 28.955 degrees, and i rounded it to 29. Then I multiplied 29/360 by 100pi(The area of the circle) And got 145pi/18. Using the Pythagoras therom and the multiplying by two, I found the area of the circle segment for circle A. What I got was {(145pi)-[SQRT(93.75) x 36]}/9. Using the exact same method for Circle B I got the area the Circle Segment as {(442.5pi)-[90 x SQRT(195)]}/72. So then add these two answers up I got: {(1602.5pi)-[228 x SQRT(93.75)]-[90 x SQRT(195)]}/72. After I got the area of Circle A(100pi) and subtract it from {(1602.5pi)-[228 x SQRT(93.75)]-[90 x SQRT(195)]}/72. I did the same with Circle B. Then I subtracted the two answers and got my final answer of: 75pi.

 

[Deleted member 4993]

Draw the picture first.

Let common area be "C".

Let the area of the bigger circle without "C" be "B"

Let the area of the smaller circle without "C" be "S"

You need to find "B - S"

In this case it is much simpler!

The area of the little circle = S + C = 25 * π

The area of the big circle = B + C = 100 * π

Then

B - S = (B+C) - (S+C) = (100 - 25) * π = 75 * π

 

[MathStudent1999]

In this case it is much simpler!

The area of the little circle = S + C = 25 * π

The area of the big circle = B + C = 100 * π

Then

B - S = (B+C) - (S+C) = (100 - 25) * π = 75 * π

Thanks so much!