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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

The volume of a right circular cone is V = 1 3 π r 2 h , where r is the radius of the base and h is the height.

(a) Find the rate of change of the volume with respect to the height if the radius is constant.

(b) Find the rate of change of the volume with respect to the radius if the height is constant.

To determine

(a)

To find: The rate of change of the volume with respect to the height if the radius is constant

Explanation

By differentiating volume of cone with respect to h using differentiation rules

1) Formula:

(i) Constant multiple rule:

ddxCf(x)=Cddx(fx)

2) Given:

V=13πr2h

3) Calculation:

Consider the function,

V=13πr2h

To find rate of change of the volume with respect to the height differentiate function with respect to h,

dVdh=ddh(

To determine

(b)

To find:The rate of change of the volume with respect to the radius if the height is constant

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