When granular materials are allowed to fall freely, they form conical (cone-shap

Question

When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of scope, measured from the horizontal, at which the loose material comes to rest is called the angle of repose and varies for different materials. The angle of repose 0 is related to the height h and oasis radius r of the conical pile by the equation 0 = cot'. A certain granular material forms a cone-shaped pile with a height of 19 feet and a base diameter of 30 feet. What is the height of a pile that has a base diameter of 104 feet? 65.8b ft 51.71 ft 66.18 ft 56.81 ft

Explanation / Answer

Given r = 15 feet h = 19 feet

= cot^-1(15/19)
= 0.9025 rad
= 51.7°

Now cot = r/h

and r = 104/2 = 52 feet and h = ?

cot 51.7 = 52/h

h = 65.84 feet

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