Question

A liquid vessel which is initially empty is in the form of an inverted regular hexagonal pyramid with altitude 25 ft. and base edge 10 ft. How much will the surface rise when 6779 liters of water is added?

Answer 1

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

Answer 2

@perl Ill leave this to you.

Answer 3

can you explain how did they get 10/25 in this

Answer 4

one moment, reading this

Answer 5

but since its a regular polygon base , and the apex is the altitude, the angle that it is off from true vertical makes this a valid proportion.

Answer 6

so the point in the middle goes to the bottom is the 25ft?

Answer 7

technically , yes