Planet Comparison

Algebra Level 3

My home planet of Brilliantia is completely smooth and you can drive from any point to another in a straight line.

To go from Brilliantopolis to Brilliantown, 2000 km away, I chose to drive straight north while my friend preferred to travel eastwards only.

How many times is the volume of Earth larger than the volume of Brilliantia?

10 100 1000 10000

Romain Bouchard by Romain Bouchard , 34, France

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1 solution

Romain Bouchard
Dec 16, 2017

The only way my friend and I can both go from Brilliantopolis to Brilliantown while driving in perpendicular direction (keep in mind we're on a sphere) is if the two cities are the antipodal point of each other, i.e. the circumference of Brilliantia is 2 × 2000 = 4000 2 \times 2000 = 4000 km as opposed to 40000 40000 km for Earth. Since the volume of a sphere is proportional to the cube of its circumference, Earth can contain ( 40000 4000 ) 3 = 1000 (\frac{40000}{4000})^3 = 1000 times Brilliantia.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I think there's a problem with the question. If you're going straight north for half the circumference, then you must have started at the south pole and ended at the north pole. But your friend can't go from the south pole to the north by going east.

Joe Mansley - 1 month, 3 weeks ago

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