Design the optimal cylindrical container (Fig. P16.1) that is open at one end and has walls of negligible thickness. The container is to hold
FIGURE P16.1
The design of the optimal cylindrical container to hold
Answer to Problem 1P
Solution: The optimal design of the optimal cylinder has radius and height same and its values is
Explanation of Solution
Given Information:
The volume of the cylinder is
Formula used:
Write the expression of surface area of a cylindrical container.
Here,
Write the expression of volume of a cylindrical container.
Calculation:
Recall the expression of volume of a cylindrical container.
The container holds
Rearrange the expression of volume for height
Recall the expression of surface area of a cylindrical container.
Substitute
To find the conditions to minimize the area solve
Solve further,
Volume of the container remains constant therefore, substitute the value of
Therefore, the value of height and radius are same to obtain to minimize the surface areas.
Substitute
Therefore, the value of the radius and the height to obtain the maximum surface area is
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Chapter 16 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
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