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28 Sep 2024, 10:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
57% (00:48) correct
42% (00:27) wrong based on 7 sessions
History
Date
Time
Result
Not Attempted Yet
The area of circle W is 16π and the area of circle Z is 4π. What is the ratio of the circumference of W to the circumference of Z ?
A. 2 to 1
B. 4 to 1
C. 8 to 1
D. 16 to 1
E. 32 to 1
A. 2 to 1
B. 4 to 1
C. 8 to 1
D. 16 to 1
E. 32 to 1
27 Oct 2024, 04:20
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OE
Recall that if a circle has radius r, then the area of the circle is \(πr^2\) and the circumference is \(2πr\). Since the area of circle W is \(16π\), it follows that \(πr^2 = 16π\), so \(r^2 = 16\) and \(r = 4\). Therefore the circumference of circle W is \(2π(4)\), or \(8π\). Similarly, since the areaof circle Z is \(4π\), it follows that \(πr^2 = 4π,\) so \(r^2 = 4\) and \(r = 2\). Terefore the circumference of circle Z is \(2π(2)\), or \(4π\). Tus the ratio of the circumference of W to the circumference of Z is \(8π\) to \(4π\), or 2 to 1.
The correct answer is Choice A.
Recall that if a circle has radius r, then the area of the circle is \(πr^2\) and the circumference is \(2πr\). Since the area of circle W is \(16π\), it follows that \(πr^2 = 16π\), so \(r^2 = 16\) and \(r = 4\). Therefore the circumference of circle W is \(2π(4)\), or \(8π\). Similarly, since the areaof circle Z is \(4π\), it follows that \(πr^2 = 4π,\) so \(r^2 = 4\) and \(r = 2\). Terefore the circumference of circle Z is \(2π(2)\), or \(4π\). Tus the ratio of the circumference of W to the circumference of Z is \(8π\) to \(4π\), or 2 to 1.
The correct answer is Choice A.
