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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm? 157142.857 mm3/s

The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm? 157142.857 mm3/s

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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The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm? 157142.857 mm3/s Enhanced Feedback 4 Please try again. Keep in mind that the volume of a sphere with radius r is V = nr. Differentiate this equation with respect to time dV Then, use the values from the exercise dt t using the Chain Rule to find the equation for the rate at which the volume is increasing, to evaluate the rate of change of the volume of the sphere, paying close attention to the signs of the rates of change (positive when increasing, and negative when decreasing). Have in mind that the diameter is twice the radius. Need Help? Read It
Transcribed Image Text:The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm? 157142.857 mm3/s Enhanced Feedback 4 Please try again. Keep in mind that the volume of a sphere with radius r is V = nr. Differentiate this equation with respect to time dV Then, use the values from the exercise dt t using the Chain Rule to find the equation for the rate at which the volume is increasing, to evaluate the rate of change of the volume of the sphere, paying close attention to the signs of the rates of change (positive when increasing, and negative when decreasing). Have in mind that the diameter is twice the radius. Need Help? Read It
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