17. Reason abstractly. An architect uses a cylindrical tube to shipblueprints to a client. The height of the tube plus twice its radius mustbe less than 60 cm.a. Write an expression for h, the height of the tube, in terms of r, theradius of the tube.b. Write an expression for V, the volume of the tube, in terms of r, theradius of the tube.c. Find the radius that produces the maximum volume.d. Find the maximum volume of the tube.

Answered: 17. Reason abstractly. An architect…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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17. Reason abstractly. An architect uses a cylindrical tube to ship
blueprints to a client. The height of the tube plus twice its radius must
be less than 60 cm.
a. Write an expression for h, the height of the tube, in terms of r, the
radius of the tube.
b. Write an expression for V, the volume of the tube, in terms of r, the
radius of the tube.
c. Find the radius that produces the maximum volume.
d. Find the maximum volume of the tube.

Expert Solution

part a

An architect uses a cylindrical tube to ship blueprints to a client. Given that the height of the tube plus twice it's radius must be less than 60 cm.

Let, the height of the tube is $h$ cm and radius of it's base is $r$ cm.

Therefore, $(h + 2 r) < 60$ . Considering a positive constant $α$ . Then, inequality sign can be converted into equal sign and it becomes $h = 60 - 2 r - α$

Thus, height of the tube $h$ is expressed in terms of radius $r$ by $h = 60 - 2 r - α$

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