Suppose that, for the sphere in the video, instead of being told how fast the ra dV = 4 cubic centimeters per dt the volume is increasing at a constant rate of %3D dr increasing at the instant when the radius is r = 10 centimeters? dt centimeters per second. Instead of thinking about the volume, suppose that we are interested in how th changing. Use the surface area formula S = 4rr to determine how fast the su %3D dr = 2 ce dt instant when the radius is r = 20 cm and the radius is increasing at
Suppose that, for the sphere in the video, instead of being told how fast the ra dV = 4 cubic centimeters per dt the volume is increasing at a constant rate of %3D dr increasing at the instant when the radius is r = 10 centimeters? dt centimeters per second. Instead of thinking about the volume, suppose that we are interested in how th changing. Use the surface area formula S = 4rr to determine how fast the su %3D dr = 2 ce dt instant when the radius is r = 20 cm and the radius is increasing at
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:Suppose that, for the sphere in the video, instead of being told how fast the radius is changing, we're told that
dV
= 4 cubic centimeters per second. How fast is the radius
dt
the volume is increasing at a constant rate of
%3D
dr
increasing at the instant when the radius is r = 10 centimeters?
dt
%3D
centimeters per second.
Instead of thinking about the volume, suppose that we are interested in how the surface area of the sphere is
changing. Use the surface area formula S = 4rr² to determine how fast the surface area is changing at the
dr
= 2 centimeters per second.
dt
instant when the radius is r = 20 cm and the radius is increasing at
dS
dt
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