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18 Aug 2022, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (03:12) correct
31%
(03:34)
wrong
based on 16
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, what is the difference between the areas of the shaded regions A and B?
A. \(\frac{(35\pi - 50)}{2}\)
B. \(\frac{(35\pi - 40)}{2}\)
C. \(\frac{(65\pi - 100)}{4}\)
D. \(\frac{(30\pi - 50)}{2}\)
E. \(\frac{(75\pi - 200)}{8}\)
Attachment:
1 (1).png [ 6.51 KiB | Viewed 1286 times ]
Are You Up For the Challenge: 700 Level Questions
18 Aug 2022, 04:08
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Large Square (LS) = 10 x 10 = 100
Small Square (SS) = 5 x 5 = 25
Large Circle (LC) = π x 5^2 = 25π
Small Circle (SC) = π x (5/2)^2 = 25π/4
The area that we are looking for is A - B
Now if we focus on SS we get
SS = B + 1/4 (LC) + 1/2(SC) - A (subtracting as A is the overlap and is counted twice)
=> A - B = 1/4 (LC) + 1/2(SC) - SS
=> A - B = 1/4 (25π) + 1/2(25π/4) - 25
=> A - B = 25π/4 + 25π/8 - 25
=> A - B = 75π/8 - 25
=> A - B = (75π - 200)/8
IMHO Option E
Small Square (SS) = 5 x 5 = 25
Large Circle (LC) = π x 5^2 = 25π
Small Circle (SC) = π x (5/2)^2 = 25π/4
The area that we are looking for is A - B
Now if we focus on SS we get
SS = B + 1/4 (LC) + 1/2(SC) - A (subtracting as A is the overlap and is counted twice)
=> A - B = 1/4 (LC) + 1/2(SC) - SS
=> A - B = 1/4 (25π) + 1/2(25π/4) - 25
=> A - B = 25π/4 + 25π/8 - 25
=> A - B = 75π/8 - 25
=> A - B = (75π - 200)/8
IMHO Option E
