Discussion
A grain heap forms at an angle of repose of \( 28 \) degrees on a bin of \( 3.0 \) m radius. The height of the surcharge cone is
Answer: D
Correct answer: 1.60 m
The heap forms a cone whose slope is the angle of repose, so its height follows from the radius:
\[ h = r \tan\theta = 3.0 \times \tan 28^\circ = 3.0 \times 0.532 = 1.60\ \mathrm{m} \]
The surcharge cone is worth calculating because it adds real capacity - here about \( 15 \) m\(^3\), or a fifth of what a cylinder of the same radius and height would hold - and because it determines the clearance needed between the fill point and the roof.
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