How many cubic yards of earth must be removed in digging an artificial lake?

Question

How many cubic yards of earth must be removed in digging an artificial lake 15ft. deep, if the level bottom is a rectangle 180ft. by 20ft. and the top is a rectangle 216ft. and 24ft.?

(pls. show your solution)

(thanks...)

Answer 1

The volume you describe is called a "frustrum of a right pyramid".  The one you describe is upside-down from the formula in my book, so I modified it to be upside-down, as well.

The formula for the area is:

Area = (Ab+At) * sqrt[H^2 + ((Bt-Bb)/2)^2] +

(Bb+Bt) * sqrt[H^2 + ((At-Ab)/2)^2]

where:

Ab is the bottom length: 180 ft

At is the top length: 216 ft

Bb is the bottom width: 20 ft

Bt is the top width: 24 ft

H is the height: 15 ft

Important: AFTER you calculate the cubic FEET... you need to divide that number by 27 to get cubic YARDS.

.