Hello, Tascja!

Sand is being poured onto a conical pile at the rate of 9 m³/hr.

Friction forces in the sand are such that the slope of the sides of the conical pile is always 2/3. Code:

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The volume of a cone is: .

We are told that the ratio: .

a. How fast is the altitude increasing when the radius of the base of the pile is 6 m?

We have: .

Since

Differentiate with respect to time: . **[1]**

When . . . and we are given: .

Substitute into **[1]**: .

Therefore: . m/hr.

b. How fast is the radius of the base increasing when the height of the pile is 10 m?

We have: .

Since

Differentiate with respect to time: . **[2]**

When . . . and we are given: .

Substitute into **[2]**: .

Therefore: . m/hr.