4. The surface area A of a sphere with radius r is given by the geometric equation A = 4ar². (a) What do the differentials 4 and represent in words? (b) Differentiate both sides of the geometric equation with respect to time to get a relationship between the differentials A and 4. (c) In class, we used the formula V = Tr3 for the volume of a sphere to find the relationship AP = T. 4ar? . Suppose a balloon is being inflated at a rate of a cm³ per second, so Compute the differential 4. AP (d) What is the rate of change of the surface arca of the balloon when the radius is 8cm? (c) As time passes, the balloon is inflated, and the radius r increases. What happens to A over time? Docs this match your intuition? dt
4. The surface area A of a sphere with radius r is given by the geometric equation A = 4ar². (a) What do the differentials 4 and represent in words? (b) Differentiate both sides of the geometric equation with respect to time to get a relationship between the differentials A and 4. (c) In class, we used the formula V = Tr3 for the volume of a sphere to find the relationship AP = T. 4ar? . Suppose a balloon is being inflated at a rate of a cm³ per second, so Compute the differential 4. AP (d) What is the rate of change of the surface arca of the balloon when the radius is 8cm? (c) As time passes, the balloon is inflated, and the radius r increases. What happens to A over time? Docs this match your intuition? dt
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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Transcribed Image Text:1. The surface arca A of a sphere with radius r is given by the geometric equation A = 4ar².
(a) What do the differentials 44 and represent in words?
(b) Differentiate both sides of the geometric equation with respect to time to get a relationship between
the differentials dA and .
(c) In class, we used the formula V
* = 1ar2. Suppose a balloon is being inflated at a rate of a cm³ per second, so = 1.
Compute the differential 44.
Tr for the volume of a sphere to find the relationship
dt
(d) What is the rate of change of the surface area of the balloon when the radius is 8cm?
(c) As time passes, the balloon is inflated, and the radius r increases. What happens to 4 over time?
Does this match your intuition?
dt
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