SOLUTION: cleopatra's needle consists of a frustum of a pyramid surmounted by a pyramid. the frustum has square bases. the upper base measures 4 ft.on a side and lower base measures 7.5 ft.

Algebra ->  Surface-area -> SOLUTION: cleopatra's needle consists of a frustum of a pyramid surmounted by a pyramid. the frustum has square bases. the upper base measures 4 ft.on a side and lower base measures 7.5 ft.       Log On


   

Question 1058156: cleopatra's needle consists of a frustum of a pyramid surmounted by a pyramid. the frustum has square bases. the upper base measures 4 ft.on a side and lower base measures 7.5 ft. on a side: the altitude of the frustum is 61 ft. find the weight of the frustum, if it is made of stone which weighs 170 lb. per cu. ft.
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the frustum is:

V+=+%281%2F3%29%28a%5E2+%2B+ab+%2B+b%5E2%29h

where a and b are the lengths of the sides of the square bases, and h is the altitude.

For this particular frustum, the volume is:

V = 1/3(4^2 + 4(7.5) + (7.5)^2)(61) = 2,079.08 cubic feet

With a density of 170 lb. per cubic foot, the total weight is:

(2,079.08 cu. ft.)(170 lb / cu. ft.) = 353,443.6 lb