A liquid vessel which is initially empty is in the form of an inverted regular hexagonal pyramid of altitude 25 feet and base edge 10 feet. By how much will the surface rise when 6,779 liters of water is added?

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Mathematics

23 September, 12:51

A liquid vessel which is initially empty is in the form of an inverted regular hexagonal pyramid of altitude 25 feet and base edge 10 feet. By how much will the surface rise when 6,779 liters of water is added?

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Davian Burns · Answer 1

Since: v = sqrt (3) / 2 s^2h

6779 liters x 0.0353cu ft/1 liter = 239.299 cu ft

but by proportion s/h = 10/25

s = 10/25 h

and v = sqrt (3) / 2 (10/25 h) ^2 h

239.299 = 0.139 h^3

h = (239.299/0.139) ^ (1/3) = 11.985 ft