Gravels are dumped from a conveyer from a height above at the rate of 1 cubic meter per minute. These gravels form a cone-shaped pile on the ground below. It is estimated that the diameter of the cone is about the same as its height. How fast is the height of the pile changing at the time of 10 minutes?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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  1. Gravels are dumped from a conveyer from a height above at the rate of 1 cubic meter per minute. These gravels form a cone-shaped pile on the ground below. It is estimated that the diameter of the cone is about the same as its height. How fast is the height of the pile changing at the time of 10 minutes?
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Given that the rate of dumping the gravel is 1m3/min. The gravel forms a cone shape whose diameter is same as that of the height.
We have to find the rate at which the height of the cone is changing at 10 minutes.

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