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16 Sep 2014, 00:40
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If the Earth's orbit around the Sun is a circle, by how much will the length of the Earth's orbit increase if the radius of this orbit grows by \(\frac{\pi}{2}\) meters?
A. 1 meter
B. 2 meters
C. \(\pi\) meters
D. \(2\pi\) meters
E. \(\pi^2\) meters
A. 1 meter
B. 2 meters
C. \(\pi\) meters
D. \(2\pi\) meters
E. \(\pi^2\) meters
16 Sep 2014, 00:40
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Official Solution:
If the Earth's orbit around the Sun is a circle, by how much will the length of the Earth's orbit increase if the radius of this orbit grows by \(\frac{\pi}{2}\) meters?
A. 1 meter
B. 2 meters
C. \(\pi\) meters
D. \(2\pi\) meters
E. \(\pi^2\) meters
Let \(R\) be the radius of the orbit. The difference in length between the current orbit and the hypothetical one will be \(2\pi(R + \frac{\pi}{2}) - 2 \pi R = 2 \pi \frac{\pi}{2} = \pi^2\)
Answer: E
If the Earth's orbit around the Sun is a circle, by how much will the length of the Earth's orbit increase if the radius of this orbit grows by \(\frac{\pi}{2}\) meters?
A. 1 meter
B. 2 meters
C. \(\pi\) meters
D. \(2\pi\) meters
E. \(\pi^2\) meters
Let \(R\) be the radius of the orbit. The difference in length between the current orbit and the hypothetical one will be \(2\pi(R + \frac{\pi}{2}) - 2 \pi R = 2 \pi \frac{\pi}{2} = \pi^2\)
Answer: E
