Quiz & Worksheet - Optimization Problems in Calculus

Instructions:

Choose an answer and hit 'next'. You will receive your score and answers at the end.

question 1 of 3

A cylindrical container must hold 2L or 2,000 cm^3 of liquid. Which of the the following is the optimization equation in terms of the radius, r, if the amount of material used to make the container is to be minimized?

Surface area = 2 * pi * r^2 + 4,000 / r Volume = pi * r^2 * h

Volume = 2 * pi * r + 4,000r^2 Surface area = 2 * pi* r^2 - 4,000

Worksheet

Print Optimization Problems in Calculus: Examples & Explanation Worksheet

1. A cylindrical container must hold 2L or 2,000 cm^3 of liquid. Find the dimensions of the container which will minimize the amount of material needed.

r = 13.65 cm; h = 6.83 cm
r = 6.83 cm; h = 13.65 cm
r = 17.84 cm; h = 2.00 cm
r = 6.83 cm; h = 6.83 cm

2. A box with a square base and a top is to be constructed from 10 square meters of material. Find the dimensions which will maximize the volume that the box can hold.

l = 1.67 m; w = 1.67 m; h = .66 m
l = 2 m; w = 2 m; h = .25 m
l = 2.58 m; w = 2.58 m; h = 1.29 m
l = 1.29 m; w = 1.29 m; h = 1.29 m

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About This Quiz & Worksheet

This quiz and attached worksheet will help to gauge your understanding of optimization problems in calculus. You'll be tested on the rules of calculus and get some optimization practice problems on which to gauge your skills.

Quiz & Worksheet Goals

Use these assessment tools to assess your knowledge of:

The formula for surface area and its proper application
Derivative equations of optimization problems
Dimensional aspects of volume in theory and in financial circumstances

Skills Practiced

This worksheet and quiz let you practice the following skills:

Critical thinking - apply relevant concepts to examine information about optimization problems in calculus in a different light
Problem solving - use acquired knowledge to solve math with optimization problems in calculus practice problems
Interpreting information - verify that you can read information regarding optimization problems in calculus and interpret it correctly
Knowledge application - use your knowledge to answer questions about optimization problems in calculus

Additional Learning

To learn more, review the corresponding lesson, called Optimization Problems in Calculus: Examples & Explanation, which covers the following topics:

Defining optimization problems
Identify absolute minimum or maximum value of a function over a given interval
Contrast and compare optimization equation and constraint equations
Understanding the substitution method
Understanding the power rule of differentiation
Defining intervals

Optimization Problems in Calculus: Examples & Explanation