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05 Nov 2021, 08:15
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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:
35%
(medium)
Question Stats:
74% (02:16) correct
26%
(02:28)
wrong
based on 53
sessions
History
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Time
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Not Attempted Yet
Two plots, one square and the other, circular, were equal in areas. If the cost of fencing the square plot and the circular plot were $2 per feet and $3 per feet respectively, what was the ration of the cost of fencing the square plot to that of the circular plot?
A. \(\sqrt{π} : 1\)
B. \(4\sqrt{π} : 3\)
C. \(4 : \sqrt{π}\)
D. \(3\sqrt{π} : 4\)
E. \(4 : 3 \sqrt{π}\)
A. \(\sqrt{π} : 1\)
B. \(4\sqrt{π} : 3\)
C. \(4 : \sqrt{π}\)
D. \(3\sqrt{π} : 4\)
E. \(4 : 3 \sqrt{π}\)
05 Nov 2021, 08:34
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Bunuel
Breaking Down the Info:
We are given a relationship about the areas. We can turn that into a relationship about the lengths.
Set the length of the square as \(s\) and the radius of the circle as \(r\).
Since the areas are equal, we have \(s^2 = \pi *r^2\). We may square root this to get \(s = \sqrt{\pi}*r\).
The cost of fencing is related to Perimeter * Cost Per Length (for the circle, that would be Circumference * Cost Per Length).
Then the ratio of the cost of fencing the square plot to that of the circular plot is:
\(\frac{\text{Perimeter of Sq} * 2 }{ \text{Circumf of Circle} * 3} = \frac{4s * 2 }{ 2 \pi r*3}\).
Now we may plug in the relation we found earlier, \(s = \sqrt{\pi}*r\), to get:
\(\frac{8*\sqrt{\pi}*r}{6 \pi r} = \frac{4}{3\sqrt{\pi}}\).
Answer: E
23 May 2025, 22:30
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