Explanation Given information: Radius ‘r’, height ‘h’ and Volume ‘V’ of cylinder are function of time. And Volume of cylinder is always constant. Concept and Formula Used: The following differentiation formula are used: d d x ( x n ) = n x n − 1 , Volume of cylinder is V = π r 2 h Calculation: The Volume of cylinder is V = π r 2 h Then r 2 = V π h Differentiate both sides with respect to ‘t’ d d t ( r 2 ) = d d t ( V π h ) d d t ( r 2 ) = V π d d t ( h ) − 1 (as V is constant) Using d d x ( x n ) = n x

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.5, Problem 18C

To determine

To write: The value of drdt in terms of r,h&dhdt

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Chapter 3.5, Problem 17C

Chapter 3.5, Problem 19S

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Chapter 3 Solutions

Loose-leaf Version for Calculus

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