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#Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is 20 cm, how fast is the surface area of the halloon increasing ? V=まTレ。 Surface avea = %3D

#Ś A spherical balloon is filled with helium at a rate of 200 cmsec.At the moment when the radius is 20 cm, how fast is the surface area of the halloon increasing ? V=まTレ。 Surface avea = %3D

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
**Problem #5: Rate of Increase of Surface Area of a Spherical Balloon** A spherical balloon is being filled with helium at a rate of 200 cm³/sec. At the moment when the radius is 20 cm, how fast is the surface area of the balloon increasing? **Formulas:** - Volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) - Surface area of a sphere: \( \text{Surface area} = 4 \pi r^2 \) This problem requires finding the rate at which the surface area of the balloon is increasing when the volume is being filled at a constant rate, and the radius at that moment is 20 cm. To solve this, we need to use calculus to relate the change in volume to the change in surface area over time.
Transcribed Image Text:**Problem #5: Rate of Increase of Surface Area of a Spherical Balloon** A spherical balloon is being filled with helium at a rate of 200 cm³/sec. At the moment when the radius is 20 cm, how fast is the surface area of the balloon increasing? **Formulas:** - Volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) - Surface area of a sphere: \( \text{Surface area} = 4 \pi r^2 \) This problem requires finding the rate at which the surface area of the balloon is increasing when the volume is being filled at a constant rate, and the radius at that moment is 20 cm. To solve this, we need to use calculus to relate the change in volume to the change in surface area over time.
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