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An Unexpected View Mystery Cache

Hidden : 9/1/2020
Difficulty:
5 out of 5
Terrain:
2 out of 5

Size: Size:   regular (regular)

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Geocache Description:


The Cache is Not at the Posted Coordinates!

The Cache

This cache is placed in a spot with (in my opinion) a fantastic and unexpected view. I hope it is well worth the puzzle. 


The Puzzle

A infinite herd of perfectly spherical cows of every possible real-valued radius is passing by a perfectly conical lake in single file line. Each cow swims in the lake and displaces a certain amount of water once it comes to rest flush against the sides of the lake. Depending on the radius, the cow could be entirely submerged, or partially submerged.

There is a single cow for which the maximum possible amount of water is displaced. The question is, what radius does this cow have and how much water does this cow displace?

This conical lake is filled to the top with a depth of exactly 1.4914 meters from the vertex to the surface. The lake has a semivertical angle of exactly 61.692 degrees.

The cache coordinates can be found with the following description: The radius of this special cow is the number of minutes north the cache is of N51°, and the volume of water displaced is the number of minutes west the cache is of W114°.

Good luck!

Congrats to brendan714 for the FTF!


You can validate your puzzle solution with certitude.

 

Additional Hints (Decrypt)

Lbh arrq gb xabj onfvp pnyphyhf gb fbyir guvf chmmyr.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)