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# Bees

## Question

On the Planet of Flowers live huge bees. In the same way as our earthly bees they deposit honey (its extraterrestrial equivalent) into the honeycombs of the shape of regular hexagonal prism. Unfortunately our expedition during a long journey back lost notes about the measurements of these honeycombs. One member of our expedition luckily (due to the fact that he weighs 80 kg and has 11-year old son) remembers that the honeycomb was 11 cm deep and that the product of greatest distance between the corners of the base (B) and the distance of opposite walls (A) was equal to 80 (distances were measured in centimeters). Could you please calculate how many liters of honey fits into one honeycomb to cover up scandalous data loss of our expedition? Edited by Thorak

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The attachment you included is broken...so I don't know if my assumption on the description of the problem is correct, but assuming I read it correctly...the answer is:

1320 cm3

V = (3*sqrt(3)/2)a2h

We know from the description that h (height) = 11cm

We can use the other clues to determine a (length of a base edge) = sqrt((320/3) * sqrt(3)) / 2

So simply plugging it in, we get

V = (3*sqrt(3)/2)(320*sqrt(3)/12)(11)

V = (2880/24)(11)

V = 1320cm3

Edited by Pickett

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# Pythagorean theorem to find the length of the hexagon's side,then find the area on cm*cm of the hole hexagon then multiply it with the depth,but the one 80cm must be wrong.No triangle can have their hypotenuse equal to the other the other line ,on an 90 degrees triagle

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The attachment you included is broken...so I don't know if my assumption on the description of the problem is correct, but assuming I read it correctly...the answer is:

Hidden Content

Let the side length of the hexagon be t and the area H.
Then:
B = 2 * t (so t = B / 2)
and
H = 3 / 2 * A * t
(A * t for the rectangle formed by the base and its opposite side then add the two triangles either side that each have area 1/4 * A * t)

So:
H = 3 / 2 * A* B / 2
H = 60

So the volume is 660 cm3 which is 0.66L

Edited by Thorak

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