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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.

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.

Advanced Engineering Mathematics
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.
Transcribed Image Text: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+2r<60. Considering a positive constant α. Then, inequality sign can be converted into equal sign and it becomes h=60-2r-α

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

 

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