A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the chamber at a constant speed of 3 cm/s (see figure). What is the rate of changeof the volume of the cylinder when the piston is 11 cm from the base of the chamber?Let V, r, and h be the volume, radius, and height of a cylinder, respectively. Write an equation relating V, r, and h.(Type an exact answer, using n as needed.)Differentiate both sides of the equation with respect to t.drdh+2rrh-dtdVdtdt(Type an exact answer, using a as needed.)When the piston is 11 cm from the base of the chamber, the volume of the cylinder is changing at a rate of about(Round to the nearest hundredth as needed.)

Answered: Image /qna-images/answer/53922cfb-c3f7-48fc-a3e4-680d898f9ce3.jpg

rentiate both sides of the equation with respect to t. dV dh (P) dr +2arh dt dt dt (Type an exact answer, using a as needed.) When the piston is 11 cm from the base of the chamber, the volume of the cylinder is changing at a rate of about (Round to the nearest hundredth as needed.)

rentiate both sides of the equation with respect to t. dV dh (P) dr +2arh dt dt dt (Type an exact answer, using a as needed.) When the piston is 11 cm from the base of the chamber, the volume of the cylinder is changing at a rate of about (Round to the nearest hundredth as needed.)

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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Question

A piston is seated at the top of a cylindrical chamber with radius 5 cm when it starts moving into the chamber at a constant speed of 3 cm/s (see figure). What is the rate of change
of the volume of the cylinder when the piston is 11 cm from the base of the chamber?
Let V, r, and h be the volume, radius, and height of a cylinder, respectively. Write an equation relating V, r, and h.
(Type an exact answer, using n as needed.)
Differentiate both sides of the equation with respect to t.
dr
dh
+2rrh-
dt
dV
dt
dt
(Type an exact answer, using a as needed.)
When the piston is 11 cm from the base of the chamber, the volume of the cylinder is changing at a rate of about
(Round to the nearest hundredth as needed.)

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