Explanation Given information: It is provided that the Sun radius will be around 93 million miles and increasing at a rate of around 0.003 mph. Formula used: The steps for solving the related rate problem are: A. The Question 1. List the quantities that are related and changed with time. 2. Restate the question in the form of rate of change and write again the question using changing quantities for their derivatives. B. The Relationship 1. Make a diagram that shows the changing quantities. 2. Determine an equation or equations that relates the changing quantities. 3. Determine the derivative with respect to the equation(s) that relates the quantity to find derived equation(s), which relate the rate of change of the quantities. C. The answer 1. Make a substitution to the derived equation(s), the given values of the quantities and their derivatives. 2. Calculate the required derivative. Volume of the sphere: The Volume of the sphere whose radius is r is given by: V = 4 3 π r 3 Calculation: Consider the steps of the formula: Step 1: The problem The changing quantities are volume V and the radius r . Since, the Sun radius is increasing at a rate of around 0.003 mph Thus, The rate of change of radius is 0.002 mph . Thus, d r d t = 0.002 Also, the Sun radius will be around 67 million miles at a particular point. Thus, r = 67 × 10 6 Since, the rate at which Sun volume will be increasing will be increasing is to be determined. Thus, the above sentence can be rephrased as: What will be rate of change of V ? Thus, d V d t = ? Step 2: The relationship Consider the formula of volume of sphere V = 4 3 π r 3 Differentiate the above equation with respect to t to get: d V d t =

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

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Chapter 12.5, Problem 14E

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To calculate: The rate at which Sun’s volume will be increasing where at a particular point the Sun radius will be around 67 million miles and increasing at a rate of around 0.002 mph.

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Chapter 12 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

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The rate at which Sun’s volume will be increasing where at a particular point the Sun radius will be around 67 million miles and increasing at a rate of around 0.002 mph.

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To calculate: The rate at which Sun’s volume will be increasing where at a particular point the Sun radius will be around 67 million miles and increasing at a rate of around 0.002 mph.

Chapter 12 Solutions