3a. 3) A cylinder is changing size in a such a way that the volume remains constant 187 cubic meters. Denote the radius of thecylinder by r, and the length of the cylinder by l (both in meters), and the area of the circle on the side of the cylinder byA. At the instant l = 2 meters, the length is shrinking at a rate of 2 meters/hour. Find the value ofdtSolve the problem by performing the following steps.a)Label the diagram with the lengths r and l. 3) A cylinder is changing size in a such a way that the volume remains constant 187 cubic meters. Denote the radius of thecylinder by r, and the length of the cylinder by l (both in meters), and the area of the circle on the side of the cylinder byA. At the instant l = 2 meters, the length is shrinking at a rate of 2 meters/hour. Find the value ofdtSolve the problem by performing the following steps.a)Label the diagram with the lengths r and l.

Answered: 3) A cylinder is changing size in a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

3a.

3) A cylinder is changing size in a such a way that the volume remains constant 187 cubic meters. Denote the radius of the
cylinder by r, and the length of the cylinder by l (both in meters), and the area of the circle on the side of the cylinder by
A. At the instant l = 2 meters, the length is shrinking at a rate of 2 meters/hour. Find the value of
dt
Solve the problem by performing the following steps.
a)
Label the diagram with the lengths r and l.

Expert Solution

Solution:

The volume of the cylinder is $18 π$ cubic meters.

$V = π r^{2} l = 18 π A l = 18 π ∵ A = π r^{2}$

Differentiate the above equation with respect to t:

$A \frac{d l}{d t} + l \frac{d A}{d t} = 0 \frac{d A}{d t} = - \frac{A}{l} \frac{d l}{d t} \frac{d A}{d t} = - \frac{18 π}{l^{2}} \frac{d l}{d t} ∵ A = \frac{18 π}{l}$

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Quotient and Product$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions