Discussion
A heap of grain forms a cone of base radius \( 1.5 \) m and height \( 0.90 \) m. The angle of repose is
Answer: C
Correct answer: 31 degrees
The heap is a right circular cone, so the angle of repose is the base angle between the sloping surface and the horizontal:
\[ \tan\theta = \frac{h}{r} = \frac{0.90}{1.5} = 0.60 \]
\[ \theta = \arctan 0.60 = 30.96^\circ \approx 31^\circ \]
Use the base radius, not the diameter: taking 0.90/3.0 would give 17 degrees. A value near 30 degrees is typical of free-flowing dry cereal grain, and it rises as moisture and cohesion increase - which is why hopper walls are pitched well steeper than the measured repose angle.
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