Can a bunny pass under?
Geometry
Level
2
Stretch a rope tightly around the Earth.
Add approximately 36 inches to it and re-stretch it evenly from the Earth.
How high above the Earth's surface will the rope be now (in inches)? (Round answer to nearest integer)
The answer is 6.
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1 solution
Assume the round Earth with radius r , hence the length of the tightly stretched rope is the Earth's circumference: 2 x r x pi
The extended rope's length L when evenly stretched by delta distance from the Earth is - similarly - expressed as the circumference of the "larger Earth" of radius r + delta :
L = 2 x ( r + delta ) x pi which, after multiplying, becomes:
L = 2 x r x pi + 2 x delta x pi
-Transferring the first term to the left side, gives us:
L - 2 x r x pi = 2 x delta x pi which simplifies to:
delta = 36 = 2 x delta x pi
delta = \frac{36}{2 x pi }
The actual result is 5.73 inches, but I asked you to round it...
Hence, it is approximately 6 inches - tall enough opening for bunnies I've met around where I live...
Thank you!