At this point in the problem, by differentiating we have "related the rates" of change of V and r. Recall that weare given in the problem that the balloon is being inflated at a constant rate of 20 cubic inches per second. Towhich derivative does this rate correspond?dVA.В.dtD. None of theseFrom the above discussion, we know the value of at every value of t. Next, observe that when the diameterdVof the balloon is 12, we know the value of the radius. In the equationdtdrsubstitute these valuesdtfor the relevant quantities and solve for the remaining unknown quantity, which isdrHow fast is the radiusdtchanging at the instant when d = 12?How fast is the radius changing at the instant when d = 16?When is the radius changing more rapidly, when d = 12 or when d = 16?A. when d = 12B. when d = 16C. Neither; the rate of change of the radius is constant This problem will lead you through the steps to answer this question:A spherical balloon is being inflated at a constant rate of 20 cubic inches persecond. How fast is the radius of the balloon changing at the instant the balloon'sdiameter is 12 inches? Is the radius changing more rapidly when d = 12 or whend = 16? Why?Draw several spheres with different radii, and observe that as volume changes, theradius, diameter, and surface area of the balloon also change. Recall that the volumeof a sphere of radius r is V = ar³. Note that in the setting of this problem, bothV and r are changing as time t changes, and thus both V and r may be viewed asimplicit functions of t, with respective derivatives and dr.Differentiate both sides of the equation V = ar with respect to t (using the chainrule on the right) to find a formula for that depends on both r and .dVdtdtdt

Name: At this point in the problem, by differentiating we have "related the
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Description: At this point in the problem, by differentiating we have "related the rates" of change of V and r. Recall that weare given in the problem that the balloon is being inflated at a constant rate of 20 cubic inches per second. Towhich derivative does th

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Math

Calculus

) This problem will lead you through the steps to answer this question: A spherical balloon is being inflated at a constant rate of 20 cubic inches per second. How fast is the radius of the balloon changing at the instant the balloon's diameter is 12 inches? Is the radius changing more rapidly when d = 12 or when d = 16? Why? Draw several spheres with different radii, and observe that as volume changes, the radius, diameter, and surface area of the balloon also change. Recall that the volume of a sphere of radius r is V = ar. Note that in the setting of this problem, both V and r are changing as time t changes, and thus both V and r may be viewed as implicit functions of t , with respective derivatives and d. Differentiate both sides of the equation V = r³ with respect to t (using the chain rule on the right) to find a formula for that depends on both r and . dt di dt AP dt