SOLUTION: How many cubic yards of earth must be removed in digging an artificial lake 15 feet deep,if the level bottom is a rectangle 180 feet by 20 feet and the top is a rectangle 216 feet

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Question 1058162: How many cubic yards of earth must be removed in digging an artificial lake 15 feet deep,if the level bottom is a rectangle 180 feet by 20 feet and the top is a rectangle 216 feet by 24 feet?pls show drawing if possible thank you
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
The volume described in this problem is a truncated rectangular pyramid.

The volume is given by:

V+=+%281%2F3%29%28A1+%2B+A2+%2B+sqrt%28A1+%2A+A2%29%29%28h%29

where A1 is one base area, A2 is the other base area (it doesn't matter which is which),
and h is the height.

For this problem:

A1 = 180 * 20 = 3600

A2 = 216 * 24 = 5184

h = 15

The volume is then:

V+=+%281%2F3%29%283600+%2B+5184+%2B+sqrt%283600+%2A+5184%29%29%2815%29+=+65520

Converting 62,520 cubic feet to cubic yards gives:

(65520 cu ft)(1 cu yd / 27 cu ft) = 2,426.67 cubic yds