SOLUTION: A box with a top is to be constructed out of a 12 by 18 inch piece of cardboard by cutting congruent squares from two of the four corners and rectangles from the other two corners,
Algebra.Com
Question 981424: A box with a top is to be constructed out of a 12 by 18 inch piece of cardboard by cutting congruent squares from two of the four corners and rectangles from the other two corners, then folding up the sides (as shown below).
1. If the square in the upper left (and lower left) hand corners is 2 inches:
What is the length of the box? ____________________.
What is the width of the box? _____________________.
What is the height of the box? _____________________.
What is the volume of the box? _____________________.
2. If the square in the upper left (and lower left) hand corners is x-inches, write a function V(x) for the volume of the box.
V(x) = ____________4x^-60x^2+216x___________
3. What values of x (the size of the cut out square) make sense to the problem?
x = ___________________________
4. What size should the cut-out square be to make the volume 400 cubic inches?
Cut out square = _______________________.
5. Find how large the cut-out squares should be to maximize the volume of the box.
Cut-out square size that maximez volume ___________________.
What is that maximum value (volume)? _____________________.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Shown where?
RELATED QUESTIONS
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by ankor@dixie-net.com)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by ankor@dixie-net.com,nyc_function)
A box with no top is to be constructed from a piece of cardboard whose length measures 12 (answered by josmiceli)
A box with no top is to be constructed from a piece of cardboard whose length measures 12 (answered by TimothyLamb)
An open top box is to be constructed out of a 85 inch by 120 inch piece of cardboard by... (answered by greenestamps)
An open top box is to be constructed out of a 75 inch by 90 inch piece of cardboard by... (answered by ikleyn)
Hello.
I'm having some trouble figuring out the following problem:
A box with a... (answered by nerdybill)
A box with an open top is to be constructed from a rectangular piece of a cardboard with... (answered by Cromlix)
A box with an open top is to be constructed from a rectangular piece of cardboard with... (answered by oberobic)
A box with no top is to be constructed from a piece of cardboard whose length measures 10 (answered by ikleyn)