Explanation Given: The radius of the spherical ball r = 25 cm . Formula used: Volume of the sphere V ( r ) = 4 3 π r 3 Surface area of the sphere A ( r ) = 4 π r 2 Linear approximation of Δ f : If f is differentiable at x = a and Δ x is small then Δ f ≈ f ′ ( a ) Δ x Where Δ f = f ( a + Δ x ) − f ( a ) . Calculation: Let r be the radius of the spherical ball. Volume of the sphere V ( r ) = 4 3 π r 3 Surface area of the sphere A ( r ) = 4 π r 2 The radius of the spherical ball r = 25 cm . It is accurate to within 0.5 cm. So, Δ r = 0.5 . Since, the maximum error in the volume is Δ V = V ( 25.5 ) − V ( 25 ) Since, the maximum error in the surface area is Δ A = A ( 25.5 ) − A ( 25 ) Find the derivative of the function V ( r ) with respect to r . V ′ ( r ) = 4 3 π 3 r 3 − 1 = 4 π r 2 Now, apply the linear approximation with r = 25 and Δ r = 0

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Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.1, Problem 47E

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Find the maximum error in the volume and surface area if r is accurate to within 0.5 cm.

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Chapter 4.1, Problem 46E

Chapter 4.1, Problem 48E

Chapter 4 Solutions

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Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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