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03 Sep 2018, 05:46
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B
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Difficulty:
45%
(medium)
Question Stats:
68% (01:49) correct
32%
(01:59)
wrong
based on 19
sessions
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A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of \(x\) meters per second. If it takes the pond \(y\) seconds to fully drain, what was its initial circumference?
A. \(\frac{2\pi y}{x}\)
B. \(\pi xy\)
C. \(\frac{\pi xy}{2}\)
D. \(2\pi xy\)
E. \(4\pi xy\)
A. \(\frac{2\pi y}{x}\)
B. \(\pi xy\)
C. \(\frac{\pi xy}{2}\)
D. \(2\pi xy\)
E. \(4\pi xy\)
03 Sep 2018, 05:46
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Official Solution:
A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of \(x\) meters per second. If it takes the pond \(y\) seconds to fully drain, what was its initial circumference?
A. \(\frac{2\pi y}{x}\)
B. \(\pi xy\)
C. \(\frac{\pi xy}{2}\)
D. \(2\pi xy\)
E. \(4\pi xy\)
We’ll go for ALTERNATIVE because there are variables in all the answers.
If we pick \(x = 1\) and \(y = 2\), it takes 2 seconds for the pool to drain, and each second represents 1 meter of the diameter, so the diameter is 2 × 1 = 2 meters long. Since the circumference is \(\pi × diameter\), the circle’s circumference is \(\pi × 2 = 2\pi\). Let’s check the answers: (A) \(\pi\) − No!; (B) \(2\pi\) − possible, but we must check the other answer choices; (C) \(\pi\) – Nope!; (D) \(4\pi\) – No!; (E) \(8\pi\) – Eliminated! We are left with answer choice (B).
Answer: B
A circular pond is drained through a tiny hole in its middle, such that its diameter becomes smaller at a constant rate of \(x\) meters per second. If it takes the pond \(y\) seconds to fully drain, what was its initial circumference?
A. \(\frac{2\pi y}{x}\)
B. \(\pi xy\)
C. \(\frac{\pi xy}{2}\)
D. \(2\pi xy\)
E. \(4\pi xy\)
We’ll go for ALTERNATIVE because there are variables in all the answers.
If we pick \(x = 1\) and \(y = 2\), it takes 2 seconds for the pool to drain, and each second represents 1 meter of the diameter, so the diameter is 2 × 1 = 2 meters long. Since the circumference is \(\pi × diameter\), the circle’s circumference is \(\pi × 2 = 2\pi\). Let’s check the answers: (A) \(\pi\) − No!; (B) \(2\pi\) − possible, but we must check the other answer choices; (C) \(\pi\) – Nope!; (D) \(4\pi\) – No!; (E) \(8\pi\) – Eliminated! We are left with answer choice (B).
Answer: B
