Question

7. The largest of the Great Pyramids in Egypt was built with a square base,

having edges that measured 754 feet and a height of 481 feet. Today, after
years of erosion, the base edges are 745 feet and its height is 471 feet. To the
nearest cubic foot, find the difference between the original and current
volumes of the pyramids.
Please show work

Answer 1

Difference between the original and current volumes = 4013140.30 cubic feet

Explanation:

Largest pyramid has the square base with one edge = 754 feet

Area of the square base = (Side)²

= (754)²

= 568516 square feet

Volume of the pyramid =
`(1)/(3)(\text{Area of the base})(\text{Height})`

=
`(1)/(3)* 568516* 481`

= 91152065.3 cubic feet

After erosion,

Area of the base = (745)² = 555025 square feet

Volume of the pyramid =
`(1)/(3)(555025)(471)`

= 87138925 cubic feet

Difference between the original and current volumes of the pyramid

= 91152065.30 - 87138925

= 4013140.30 cubic feet