Comparing Grow Rates of Exponential and Logarithmic Functions and Their Applications in Engineering

October 16, 2024October 16, 2024 Discipline: Calculus

Work through the problem:  

 
You are designing a juice container that has the shape of a right circular cylinder ( see image and formulas attached). The container is supposed to hold 6 cubic inches juice. Find the dimensions that will use a minimum amount of construction material.

1. (Representation of Evidence, Organize ) Analyze the problem. From the information provided, what can you say about the volume of this juice box? Can you find a relationship between the variables r and h? 

2. (Define or Interpret the Problem ) What are you asked to minimize? Formulate the problem (use derivatives). Explain your formulation.

3 (Calculation) Perform the necessary calculation on equation(s) in step 2 to find the minimum dimensions.

4. (Communication) Summarize your results.

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