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 ->
Customizable Word Problem Solvers
-> Evaluation
-> 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,
Log On
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)? _____________________.
