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21 Oct 2020, 00:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:47) correct
38%
(03:05)
wrong
based on 122
sessions
History
Date
Time
Result
Not Attempted Yet
On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (\(0, −2 \sqrt{2}\)) and (\(2 \sqrt{2}, 0\)). What is the area of the region, rounded to the nearest tenth, that is inside the square but outside the circle?
A. 3
B. 3.2
C. 3.4
D. 3.6
E. 3.8
A. 3
B. 3.2
C. 3.4
D. 3.6
E. 3.8
21 Oct 2020, 02:04
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Another brillient question by Bunuel
diagonal of square is = 2√2+2√2= 4√2
Hence side of the sq will be 4 because diag in square is a√2
area of sq = 4 * 4 = 16
just pay attention to circle which is in the square , the diameter of the the circle will be side of sq. i.e = 4
Hence radius will be = 2
area of sq= pi * 2^2 = 3.14 * 4 = 12.56 = 12.6 ( nearest to tenth)
Hence desired area that is inside the square but outside the circle is = area of sq - an area of circle = 16- 12.6 = 3.4
Hence IMO answer will be C = 3.4
Please see the attachment for the diagram for clear understanding.
diagonal of square is = 2√2+2√2= 4√2
Hence side of the sq will be 4 because diag in square is a√2
area of sq = 4 * 4 = 16
just pay attention to circle which is in the square , the diameter of the the circle will be side of sq. i.e = 4
Hence radius will be = 2
area of sq= pi * 2^2 = 3.14 * 4 = 12.56 = 12.6 ( nearest to tenth)
Hence desired area that is inside the square but outside the circle is = area of sq - an area of circle = 16- 12.6 = 3.4
Hence IMO answer will be C = 3.4
Please see the attachment for the diagram for clear understanding.
Bunuel
Attachments
File comment: Diagram
Attachment-1.jpeg [ 137.08 KiB | Viewed 6459 times ]
General Discussion
21 Oct 2020, 02:11
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Given
To Find
• The area of the region, rounded to the nearest tenth, that is inside the square but outside the circle.
Approach and Working Out
Correct Answer: Option C
- • On a rectangular coordinate plane, a circle centered at (0, 0) is inscribed within a square with adjacent vertices at (0, 2√2) and (2√2, 0).
To Find
• The area of the region, rounded to the nearest tenth, that is inside the square but outside the circle.
Approach and Working Out
- • If you consider the diagram below,
- o The side of the square is the distance between (0, 2√2) and (2√2, 0).
o We can calculate it as 4.
o PQ will be 4 and thus radius will be 2.
• Area of the required region = Area of the square – Area of the circle.
- o Area of the square = 16 square units.
o Area of the circle = π\(2^2\) = 4π = 4×3.14 = 12.56
o Answer = 16 – 12.56 = 3.44
o ~ 3.4
Correct Answer: Option C
Attachments
GC_CG.png [ 26.04 KiB | Viewed 6299 times ]
