Ask HN: Solve this FoundersFund problem
A sphere has a diameter of 2,160 meters. How many meters long is “Unit X” if the surface of the sphere, measured in square Units X is equal to the volume of the sphere measured in cube Units X? Round to the nearest whole number, and enter the number only.
Radius r = 1080 meters.
Volume of a sphere = (4/3) * pi * r^3
Surface area of a sphere = 4 * pi * r^2
We want to find x, some unit of measure.
The volume of the sphere in units of x^3 is:
((4/3) * pi * r^3) / x^3
The surface area of the sphere in units of x^2 is:
(4 * pi * r^2) / x^2
The problem states these are equal. So:
((4/3) * pi * r^3) / x^3 = (4 * pi * r^2) / x^2
(1/3) * r = x
360 = x
1741
360