A retangular excavation measured 20ft by 30ft at the surfacemgrade. if the side slope is 1:2 and excavation is

Question

12ft deep, find the total material to be removed in cubic yards.

Answer 1

(6+30)/2 x 12 x20  = 4320 ft^3

4320/27 = 160 yrd^3

Answer 2

I hope I can get the 1:2 part right. Is it 1 horizontal to 2 vertical? that means the slope ends 6 ft out from the bottom.

so the rectangular portion is 20-12 by 30-12 by 12 or 8x18x12 or 1728 ft³

the angled portions, not counting the corners, is

½ x 2 x 12 x 6 x 18 = 1296 for the long sides and

½ x 2 x 12 x 6 x 8  = 576 for the short sides

(½ because of the slope, 2 because there are 2 sides)

this totals 1872 ft³

This leaves the corners.  It depends on how the dirt piles, but I'll guess at 1/4 the volume since it is piling in from both sides.

Each corner is 6x6x12

so 4 x 1/4 x 6x6x12 = 432 ft³

adding it all up, 1728 + 1872 + 432 = 4032 ft³

4032 / 27 = 150 yd³