A Zoo Is Designing a Giant Bird Cage Consisting of a Cylinder

question 71

Essay

A zoo is designing a giant bird cage consisting of a cylinder of radius r feet and height h feet with a hemisphere on top (no bottom).The material for the hemisphere costs $20 per square foot and the material for the cylindrical sides costs $10 per square foot; the zoo has a budget of $5120.Find the values of r and h giving the birds the greatest space inside assuming the zoo stays within its budget.

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Definitions:

P(A Or B)

The probability that either event A or event B occurs or both events occur together, a fundamental concept in probability theory.

College Professorship

A faculty position at a college or university, typically involving teaching, research, and administrative responsibilities.

Probability

A measure of the likelihood that an event will occur, expressed as a number between 0 (impossibility) and 1 (certainty).

College Professorship

A senior academic position in a college or university, involving teaching, research, and possibly administrative responsibilities.