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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
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.

(a)

To determine

To find: The rate of change of the volume with respect to the height.

Explanation

Given:

The volume of a right circular cone is V=13πr2h, Where r is constant.

Calculation:

The volume of a right circular cone is V=13πr2h.

Differentiate on both sides with respect to h.

dVdh=ddh(

(b)

To determine

To find: The rate of change of the volume with respect to the radius.

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