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Exercise 12

Avg difficulty 2.5

Sand is being dumped off a conveyor belt onto a pile in such a way that the pile forms in the shape of a cone whose radius is always equal to its height. Assuming that the sand is being dumped at a rate of 1010 cubic feet per minute, how fast is the height of the pile changing when there are 10001000 cubic feet on the pile?

Boelkins, Active Calculus, §3.1 Related rates, Exercise 12

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.