Answer:
1329.3 yd³
Explanation:
You want the volume of a cone with an offset peak such that the angle of elevation of the peak from one side of the base is 45°, and that slant height is 18 yards. The diameter of the base is 20 yards.
Height
The ratio of sides in a 45°-45°-90° triangle is 1 : 1 : √2. That is, the height of the cone is ...
h = (18 yd)/√2 ≈ 12.7 yd . . . . . rounded height value
Volume
The volume of the cone is given by ...
V = (π/3)r²h
The radius is half the diameter, so is ...
r = (20 yd)/2 = 10 yd
Then the volume is ...
V = (3.14/3)(10 yd)²(12.7 yd) ≈ 1329.3 yd³
The volume of the cone is about 1329.3 yd³.
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Additional comment
If the "pi button" on the calculator is used, and no intermediate rounding of computation results is done, the volume is computed as 1332.9 yd³.
Loose granular material rarely has an angle of repose greater than 45°. The angle on the other side of the cone is about 60.3° relative to the base.
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