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How many cubic feet of earth must be removed in digging an artificial lake 15 ft. deep, if the level bottom is a rectangle 180 ft. by 20 ft. and the top is a rectangle 202 ft. by 25 ft.?

 Feb 27, 2023
 #1
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Area of the top =202  x  25 = 5050 ft^2

 

Area of the bottom=180  x  20 = 3600 ft^2

 

Average area of the bottom and the top:

(5050  +  3,600) / 2  = 4,325 ft^2

 

Volume of earth removed:

 

15  x  4,325 =64,875 ft^3 - volume of earth to be removed.

 Mar 1, 2023
 #2
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This is the volume of a Frustrum:

 

Volume of frustum of a rectangular pyramid = h/3 * (l*w + sqrt(l*w*l1*w1) + l1*w1)

Length l: 
202

Breadth w: 
25

Length l1: 
180

Breadth w1: 
20

Height h: 
15



The calculated volume is: 64,569.0056 cu feet.

 Mar 1, 2023

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