PRACTICE: Maximizing the Volume of a Box
You are designing a box to be made of a piece of cardboard that is 10 inches by 15
inches. The box will be formed by making the square cuts shown in the diagram and
folding up the sides.
x
x
x
x
x
x
x
x
x
Volume of a Box = (Length)(Width)(Height)
Find the volumes of the boxes that can be created for the given values of x in the table
x
Volume
1
2
3
4
5
1.) Which integer value of x maximizes the volume of the box?
2.) Are there other possible values of x that that could provide a larger volume?
3.) Provide the formula for the volume of the box in terms of x.
VOLUME =
4.) Write the formula from #3 in the form
y = ax 3 + bx 2 + cx + d
!
What is the range for this problem?
VOLUME
5.) Graph the function above on your graphing calculator. Sketch the part of
graph below that makes sense in the context of the problem.
200
What is the domain for this problem?
x
6.) Use your calculator to find the value of x that maximizes the volume of the box.
PRACTICE: Maximizing the Volume of a Box
You are designing a box to be made of a piece of cardboard that is 18 inches by 16
inches. The box will be formed by making the square cuts shown in the diagram and
folding up the sides.
x
x
x
x
x
x
x
x
x
Volume of a Box = (Length)(Width)(Height)
Find the volumes of the boxes that can be created for the given values of x in the table
x
Volume
1
2
3
4
5
6
7
8
1.) Which integer value of x maximizes the volume of the box?
2.) Are there other possible values of x that that could provide a larger volume?
3.) Provide the formula for the volume of the box in terms of x.
VOLUME =
4.) Write the formula from #3 in the form
y = ax 3 + bx 2 + cx + d
!
What is the range for this problem?
VOLUME
5.) Graph the function above on your graphing calculator. Sketch the part of
graph below that makes sense in the context of the problem.
500
What is the domain for this problem?
x
6.) Use your calculator to find the value of x that maximizes the volume of the box.
PRACTICE: Maximizing the Volume of a Box