A box with a square base and open top must have a volume of 143748 cm^3. 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, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x)=? Now, calculate when the function A(x) has a minimum. The length of the side of the square bottom is ? The minimum amount of material needed is?
A box with a square base and open top must have a volume of 143748 cm^3. 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, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x)=? Now, calculate when the function A(x) has a minimum. The length of the side of the square bottom is ? The minimum amount of material needed is?
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter63: Volumes Of Pyramids And Cones
Section: Chapter Questions
Problem 25A
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A box with a square base and open top must have a volume of 143748 cm^3. 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, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in terms of x.]
Simplify your formula as much as possible.
A(x)=?
Now, calculate when the function A(x) has a minimum.
The length of the side of the square bottom is ?
The minimum amount of material needed is?
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