A box with a square base and open top must have a volume of 78732 cm'. We wish to find the dimensions of the box 3 ст that minimize the amount of material used.
A box with a square base and open top must have a volume of 78732 cm'. We wish to find the dimensions of the box 3 ст that minimize the amount of material used.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 32A: A piece in the shape of a frustum of a pyramid with regular octagon bases is 23.84 centimeters high....
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![A box with a square base and open top must have a volume
of 78732 cm'. We wish to find the dimensions of the box
that minimize the amount of material used.
First, find a formula for the surface area of the box in terms
of only x,
[Hint: use the volume formula to express the height of the
box in terms of x.]
Simplify your formula as much as possible.
the length of one side of the square base.
A(x) :
Next, find the derivative, A'(x).
A' (x)
Now, calculate when the derivative equals zero,
when A'(x) = 0. [Hint: multiply both sides by x*.]
that is,
A'(x) = 0 when x =
We next have to make sure that this value of x gives a
minimum value for the surface area. Let's use the second
derivative test. Find A"(x).
A"(x)
Evaluate A"(x) at the x-value you gave above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40d0a663-0344-40f7-a351-3ecc40f5ee39%2F50a64a12-c008-4e1c-91e9-49b7442bed38%2F6nisel6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A box with a square base and open top must have a volume
of 78732 cm'. We wish to find the dimensions of the box
that minimize the amount of material used.
First, find a formula for the surface area of the box in terms
of only x,
[Hint: use the volume formula to express the height of the
box in terms of x.]
Simplify your formula as much as possible.
the length of one side of the square base.
A(x) :
Next, find the derivative, A'(x).
A' (x)
Now, calculate when the derivative equals zero,
when A'(x) = 0. [Hint: multiply both sides by x*.]
that is,
A'(x) = 0 when x =
We next have to make sure that this value of x gives a
minimum value for the surface area. Let's use the second
derivative test. Find A"(x).
A"(x)
Evaluate A"(x) at the x-value you gave above.
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