# Optimizing Complex Systems

Instructions:

question 1 of 3

### You are designing a cylindrical package. You can spend \$4 on packaging, which costs \$0.10 square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than \$4. What are the equations for the surface area and volume of this cylinder?

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### 2. You are designing a cylindrical package. You can spend \$4 on packaging, which costs \$0.10 per square cm. You would like to determine the maximum volume that you can contain in a cylinder that costs less than \$4. What is the derivative of the equation for volume with respect to the cylinder radius?

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Check how well you understand the math skills needed to optimize complex systems with this quiz. You will need to work out the answers to math word problems in order to complete this quiz.

## Quiz & Worksheet Goals

This quiz requires you to answer questions about cylindrical packages that deal specifically with finding:

• Surface area
• Volume

## Skills Practiced

The questions included on this quiz were designed to help you practice these abilities:

• Reading comprehension - ensure that you draw the most important information from the related lesson on optimizing complex systems
• Problem solving - use acquired knowledge to solve practice problems involving the radius or maximum volume of a cylinder
• Knowledge application - use what you know to answer questions about equations related to the surface area or volume of a cylinder