Lesson: Pieces of Pi

Comment on Pieces of Pi

There are two formulas for area of circumference and area of sector are these formula are different ..... please tell me where to use them
greenlight-admin's picture

I think you might be confusing two different concepts.
There is no such thing as the AREA of the circumference. The circumference is the DISTANCE around a circle. The area of sector is the amount of space the sector occupies.

Thank you. You made it so simple to understand-sector and arc which i always found so difficult.
greenlight-admin's picture

Thanks for taking the time to say that!

great video indeed. can sector OCE mean the 360-x portion of the circle?
greenlight-admin's picture

I believe you're referring to the diagram at 2:05 in the video.

Great question!!

Yes, the notation OCE could very well be referring to the much larger (unshaded) portion of the circle.

There are two ways for the test-maker to avoid such ambiguity:

1) they might shade the desired sector, so that it's clear which portion the question is referring to

2) they might add a 4th point on the circle (e.g. add a point D BETWEEN C and D and then refer to the sector OCDE)

GRE practice question (difficulty level: 160 to 170) – Magoosh
I don't think that their answer is correct. If so, would it be possible for you to provide us with its solution? Their solution doesn't make sense to me.
greenlight-admin's picture

I'm happy to help.

I'll refer you to the diagram at https://magoosh.com/gre/2011/gre-geometry-practice-question-of-the-week-...

The 3 colored regions (blue, yellow and pink) comprise the TOTAL area that the cow can reach. So, we must ADD the areas of all the regions.

The blue region is 3/4 of a circle that has a radius of 5.
So, the area = (3/4)(π)(5²) = (75/4)π

ASIDE: π = pi

The yellow region is 1/4 of a circle that has a radius of 1.
How do we know the yellow region has radius 1?
The cow's rope has length 5, and the shed has length 4.
So, the radius of the yellow region = 5 - 4 = 1
Area = (1/4)(π)(1²) = (1/4)π

The pink region is 1/4 of a circle that has a radius of 2.
Area = (1/4)(π)(2²) = (4/4)π = π

TOTAL area = (75/4)π + (1/4)π + π
= (76/4)π + π
= 19π + π
= 20π

Does that help?


I got it now. THANK you!!!

Happy New Year!!!

Hi Brent

For the question in the video at 02:54
I had approached in this way


area of circle =360

then consider the unknown values as x then

greenlight-admin's picture

Your solution is pretty much the same as the one presented in the solution.
In the video solution, we get:
Area = (160/360)(π)(6²)
= (160/360)(36π)

In your solution, you have:
Area = (160)(36)(π)/360
= (160/360)(36π)

Both solutions work, although your may take a little longer.


How did you know the the rest if the circle was 270? How did you find the 90?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-the-figure-above-vertex-r-of-square-pqr...

We know the angle is 90°, because we're told that PQRS is a square, and all 4 angles in a square are 90°.
Since 360 degrees are in a complete circle, the measurement of the angle that's not part of the square = 360° - 90° = 270°

Does that help?


Hey brent, how can you tell that the sector RTS has the same central angle as sector QTP?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-the-figure-above-if-point-t-is-6-centim...
Since ∠RTS and ∠QTP are opposite angles, we know they're equal.

Opposite angles are covered in the following video, starting at 4:00: https://www.greenlighttestprep.com/module/gre-geometry/video/858

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