SOLUTION: the frustum has a regular hexagon on bases. the upper base measures 17 ft. on side and the lower base measures 27 ft. on a side. the altitude of the frustum is 15 ft. find the mass

Algebra ->  Bodies-in-space -> SOLUTION: the frustum has a regular hexagon on bases. the upper base measures 17 ft. on side and the lower base measures 27 ft. on a side. the altitude of the frustum is 15 ft. find the mass      Log On


   

Question 1191467: the frustum has a regular hexagon on bases. the upper base measures 17 ft. on side and the lower base measures 27 ft. on a side. the altitude of the frustum is 15 ft. find the mass of the frustum, if its density is 97 lbs. per cu. ft.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The formula for the volume of a frustum of a pyramid with bases A and B and height h is

V=%281%2F3%29%28A%2BB%2Bsqrt%28AB%29%29h

The area of a regular hexagon with side length s (viewing the regular hexagon as 6 equilateral triangles with side length s) is

6%28%28s%5E2%2Asqrt%283%29%29%2F4%29

So....

area of lower base: A=6%28%2827%5E2%2Asqrt%283%29%29%2F4%29
area of upper base: B=6%28%2817%5E2%2Asqrt%283%29%29%2F4%29

You can do the calculations:

..Calculate the base areas A and B
..Calculate the volume
..Multiply the volume by the density to get the mass