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Assume that the radius r of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V = ar?. Determine the rate at which the volume is changing with respect to time whenr= 5in. The volume is changing at a rate of |in®/min.

Assume that the radius r of a sphere is expanding at a rate of 10in./min. The volume of a sphere is V = ar?. Determine the rate at which the volume is changing with respect to time whenr= 5in. The volume is changing at a rate of |in®/min.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Assume that the radius \( r \) of a sphere is expanding at a rate of \( 10 \, \text{in./min} \). The volume of a sphere is \( V = \frac{4}{3} \pi r^3 \). Determine the rate at which the volume is changing with respect to time when \( r = 5 \, \text{in.} \) The volume is changing at a rate of \(\boxed{\phantom{0}}\) \(\text{in}^3/\text{min}\).
Transcribed Image Text:Assume that the radius \( r \) of a sphere is expanding at a rate of \( 10 \, \text{in./min} \). The volume of a sphere is \( V = \frac{4}{3} \pi r^3 \). Determine the rate at which the volume is changing with respect to time when \( r = 5 \, \text{in.} \) The volume is changing at a rate of \(\boxed{\phantom{0}}\) \(\text{in}^3/\text{min}\).
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