Explanation Given information: The volume V of a sphere is given by V ( r ) = 4 3 π r 3 The surface area S of a sphere is given by S ( r ) = 4 π r 2 Where r = radius of the sphere. Calculation: The volume V of a sphere is given by, V = 4 3 π r 3 ⇒ 3 V = 4 π r 3 ⇒ r 3 = 3 V 4 π ⇒ r = 3 V 4 π 3 = ( 3 V 4 π ) 1 3 ⇒ r ( V ) = 3 V 4 π 3 = ( 3 V 4 π ) 1 3 { Radius expressed in terms of volume of sphere } ... eq(i) Similarly, the surface area S of a sphere is given by, S ( r ) = 4 π r 2 ⇒ S = 4 π r 2 ⇒ r 2 = S 4 π ⇒ r = S 4 π = ( S 4 π ) 1 2 ⇒ r ( S ) = S 4 π = ( S 4 π ) 1 2 { Radius expressed in terms of surface area of sphere } Now let us calculate composite function S ∘ r ( V )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 1.3, Problem 33E

To determine

The radius r, as a function of volume V of a sphere.

The surface area S as a function of volume V of a sphere.

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Chapter 1.3, Problem 32E

Chapter 1.3, Problem 34E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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The radius r , as a function of volume V of a sphere. The surface area S as a function of volume V of a sphere.

Solution Summary: The author calculates the radius r, as a function of volume V of the sphere, and the surface area S.

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The radius r, as a function of volume V of a sphere.

The surface area S as a function of volume V of a sphere.

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Chapter 1 Solutions

The radius r , as a function of volume V of a sphere. The surface area S as a function of volume V of a sphere.

Solution Summary: The author calculates the radius r, as a function of volume V of the sphere, and the surface area S.

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The radius r, as a function of volume V of a sphere. The surface area S as a function of volume V of a sphere.

Want to see the full answer?

Chapter 1 Solutions

The radius r, as a function of volume V of a sphere.

The surface area S as a function of volume V of a sphere.