
Maximizing Volume of an Open-Top Box

Interactive Video
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Mathematics
•
10th - 12th Grade
•
Hard

Emma Peterson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary goal when constructing the box with a square base and open top?
Minimize the surface area
Maximize the height
Maximize the volume
Minimize the volume
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the constraint equation for the surface area of the box?
x^2 + xy = 1800
x^2 + 2xy = 1800
x^2 + 4xy = 1800
2x^2 + 4xy = 1800
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do we express the volume of the box in terms of one variable?
By solving the constraint equation for y
By solving the constraint equation for x
By solving the volume equation for x
By solving the volume equation for y
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of the volume function used to find critical points?
450 - x^2
450 - 4x^2
450 - 2x^2
450 - 3x^2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the second derivative test used in this problem?
To find the maximum surface area
To verify the critical point is a maximum
To verify the critical point is a minimum
To find the minimum volume
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of x that maximizes the volume?
10√6
10√5
10√3
10√4
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the formula for the height y in terms of x?
y = 450/x - x/4
y = 450/x + x/4
y = 450/x - x/2
y = 450/x + x/2
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