A spherical balloon is being inflated at a constant rate of 17 cubic inches per...
70.2K
Verified Solution
Link Copied!
Question
Calculus
A spherical balloon is being inflated at a constant rate of 17 cubic inches per second How fast is th radius of the balloon changing at the instant the balloon s diameter is 8 inches Is the radius changing more rapidly when d 8 or when d 12 Why equation V 4 Recall that the volume of a sphere of radius r is V Tr Note well that in the setting of this 3 problem both V and r are changing as time t changes and thus both V and r may be viewed as dV dr Differentiate both sides of the implicit functions of t with respective derivatives and dt dt 4 3 Tr with respect to t using the chain rule on the right to find a formula for dr dt dV dt Time 1 that depends on both r and dV dt Time 2 dr dt At this point in the problem by differentiating we have related the rates of change of V and r Recall that we are given in the problem that the balloon is being inflated at a constant rate of 17 cubic inches per second Is this rate the value of dr dv dt dt Time 3 or dV dt
Answer & Explanation
Solved by verified expert
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Zin AI - Your personal assistant for all your inquiries!
