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Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 12 - Problem 49
Get Full Access to Calculus: Early Transcendentals - 2 Edition - Chapter 12 - Problem 49

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# Solved: Region between spheres Two spheres have the same ISBN: 9780321947345 167

## Solution for problem 49 Chapter 12

Calculus: Early Transcendentals | 2nd Edition

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Problem 49

Region between spheres Two spheres have the same center and radii r and R, where 0 6 r 6 R. The volume of the region between the spheres is V1r, R2 = 4p 3 1R3 - r32. a. First use your intuition. If r is held fixed, how does V change as R increases? What is the sign of VR? If R is held fixed, how does V change as r increases (up to the value of R)? What is the sign of Vr? b. Compute Vr and VR. Are the results consistent with part (a)? c. Consider spheres with R = 3 and r = 1. Does the volume change more if R is increased by _R = 0.1 (with r fixed) or if r is decreased by _r = 0.1 (with R fixed)?

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##### ISBN: 9780321947345

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