# 2. At a sand and gravel plant, sand is falling off a conveyor onto a conical pile at the rate of...

## Question:

2. At a sand and gravel plant, sand is falling off a conveyor onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 15ft high?

## Rate of Change:

We will find the rate of change of height by first writing the formula for the volume of the cone and then changing the radius in terms of height and then differentiating it with respect to t and then plug-in the values.

## Answer and Explanation:

To find the rate of change of height we will first write the expression for the volume of the cone:

{eq}V=\frac{1}{3}\pi...

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from Glencoe Pre-Algebra: Online Textbook Help

Chapter 8 / Lesson 7