Help calculating 2 areas

Larkula

New member
Joined
Oct 22, 2016
Messages
2
So i'm new to maths and apparently not very good with it.
I have this two exercises where i have to calculate the area of the blue portions together as the picture below shows.
My strategy for the first one is to calculate the area of the bigger circle, divide it by 2. Then i calculate the area of the smaller circles. In the end i just subtract the smaller ones from the bigger circle. I know i'm getting it wrong because i have the final answers.
As for the second exercise i'm using the same logic but not getting anywhere close to the real answer.
Help, pretty please!
 

Attachments

  • IMG_20161023_011708 (1).jpg
    IMG_20161023_011708 (1).jpg
    99.1 KB · Views: 3
I have this two exercises where i have to calculate the area of the blue portions together as the picture below shows.

attachment.php


My strategy for the first one is to calculate the area of the bigger circle, divide it by 2. Then i calculate the area of the smaller circles. In the end i just subtract the smaller ones from the bigger circle. I know i'm getting it wrong because i have the final answers.
What were your steps? What was your final result? For instance, you noted that |AC| = 4, so the radius R of the larger (whole) circle (of which half is shaded) is R = 4. You then found the area of the entire circle (getting what value?) and then divided by 2 (getting what value?). Then you noted what must be the value of the radius r of the smaller circles. You also noted that the two unshaded half-circles form one whole (unshaded) circle. You found this circle's area (by what steps? getting what value?), and subtracted this from the area of the larger (shaded) half-circle, and... then what?

As for the second exercise i'm using the same logic but not getting anywhere close to the real answer.
On what logical basis are you using the same steps to find such a very different area?

Please be complete, showing all of your thoughts and steps. Thank you! ;)
 
My approach

So as to the first exercise:

Area of the bigger circle: pi*4^2/3 = 16 pi/2 = 8pi
Area of the smaller circle = pi*2^2/2 = 2pi

Total = 8pi-2pi-2pi= 4pi

According to the solution, i got the right answer. But is my logic flawed in any way?

As to the second exercise:

Total Area = pi*5^2/2+pi*(3/2)^2/2 +pi*2^2/2 - pi^2/2
=121pi/8

This last one is not even close to the real result which is 5.75
 
So as to the first exercise:

Area of the bigger circle: pi*4^2/3 = 16 pi/2 = 8pi
Are you raising the radius to the power "2/3"? Or divided "pi r^2" by 3? Either way, why? How do the other values follow from the first term? Are you finding the "area of the bigger circle", or just half?

Area of the smaller circle = pi*2^2/2 = 2pi
Is this actually the area of one of the smaller half-circles? I think so.

Total = 8pi-2pi-2pi= 4pi

According to the solution, i got the right answer. But is my logic flawed in any way?
If you meant "I found the area of the larger half-circle by finding (1/2)(pi)(4^2) = 8pi, and then found the area of each of the smaller half-circles by finding (1/2)(pi)(2^2) = 2pi, and then subtracting to get 8pi - 2(2pi) = 8pi - 4pi = 4pi", then your logic is correct. If you meant anything else, then I'm not sure how you got your answer.

Yes, the logic of your steps counts. Many graders would stop at "pi*4^2/3" and mark the rest wrong.

As to the second exercise:

Total Area = pi*5^2/2+pi*(3/2)^2/2 +pi*2^2/2 - pi^2/2
=121pi/8

This last one is not even close to the real result which is 5.75
What was your reasoning? How did you arrive at the posted computations? (Try showing your steps, one at a time, with their logic, similar to how I showed mine, above.) ;)
 
So as to the first exercise:

Area of the bigger circle: pi*4^2/3 = 16 pi/2 = 8pi
Area of the smaller circle = pi*2^2/2 = 2pi

Total = 8pi-2pi-2pi= 4pi

According to the solution, i got the right answer. But is my logic flawed in any way?

As to the second exercise:

Total Area = pi*5^2/2+pi*(3/2)^2/2 +pi*2^2/2 - pi^2/2
=121pi/8

This last one is not even close to the real result which is 5.75
The first answer is correct w/o any flaws--good job.

The 2nd solution has some errors. The radius of the big semi circle is not 5 as you stated above. What is it? You then subtract pi^2/2. Is the radius pi^.5?? I do not think so. Your logic is fine. It is the radii that you are using that are wrong. Just fix it and you should be ok.
Come back and show us your final result.
 
Top