Solve the problem.

When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, 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 θ is related to the height h and base radius r of the conical pile by the equation θ = cot-1(r/h). 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?

Question

Solve the problem.

When granular materials are allowed to fall freely, they form conical (cone-shaped) piles. The naturally occurring angle of slope, 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 θ is related to the height h and base radius r of the conical pile by the equation θ = cot-1(r/h). 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?

anonymous · Answer

If I'm reading that right the cotangent^-1 can also be written as 1/tan^-1  

the cone forms a triangle with height 19 feet and base 15   giving you a side angle side triangle with which to find the angle theta  and if I'm reading the problem right the theta is the same for both piles....in which case the new pile will have angle (theta)  base 52 (.5 *104) angle 90