Question

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

Answer 1

The volume of a pyramid = (1/3) * altitude* area of the base
area of a regular hexagon = (3 sqrt3 a^2) / 2 where a = length of the edgs

Answer 2

in your case a = 10, the volume = 6779 and you need to find the altitude L

Answer 3

so we have

6779 = (1/3) * L * (3 sqrt3 10^2) / 2

solve for L

Answer 4

3 sqrt a^2 is only applicable to what regular polygons? my professor teaches a different formula

Answer 5

(3 sqrt3 * a^2 )/ 2 is applicable to a regular hexagon

Answer 6

oh, I get L - 78.28

Answer 7

right

Answer 8

thats what i get too

Answer 9

Oh - but the vessel is only 25 ft high!!

Answer 10

lol it says 12 ft as the answer at the back of the book

Answer 11

theres something wrong somewhere....

Answer 12

well you need to find the height of the smaller pyramid you make by reducing the volume of the larger pyramid by 6779 I think

Answer 13

I think you need to convert 6779 liters to cubic ft

Answer 14

oh i see whats wrong - the vessel is inverted - so as you say you have to find the volume of smaller pyramid

Answer 15

sorry guy - i messed up there.

Answer 16

no you need to get the height difference i think

Answer 17

yeah - its 6779 liters not cubic feet

Answer 18

oh yeah you're right the volume lol

Answer 19

we need conversion factor for liters to cu ft

Answer 20

that's 0.0353ft^3/L

Answer 21

it's 239.3 cubic ft

Answer 22

ok