We are constructing a box from a piece of paper. The paper is a piece of “ledger-sized paper” which measures 11”x17”. We will remove a square of size “x” inches from each corner and turn up the edges. A piece of ledger paper is the same size as taping the long sides of two pieces of standard 8.5x11 paper together. Once we remove the squares of size “x” inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable “x”. h=h= w=w= l=l= What is the equation that represents the Volume of the box as a function of the cutsize of the box? V(x)=Vx= What is the restricted domain of this problem? (That is, what x values "make sense"?) ≤x≤≤x≤
We are constructing a box from a piece of paper. The paper is a piece of “ledger-sized paper” which measures 11”x17”. We will remove a square of size “x” inches from each corner and turn up the edges.
A piece of ledger paper is the same size as taping the long sides of two pieces of standard 8.5x11 paper together.
Once we remove the squares of size “x” inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable “x”.
| h=h= | ||
| w=w= | ||
| l=l= |
What is the equation that represents the Volume of the box as a function of the cutsize of the box?
V(x)=Vx=
What is the restricted domain of this problem? (That is, what x values "make sense"?)
≤x≤≤x≤
What is the restricted range of this problem? (That is, what V values "make sense"?)
≤V(x)≤≤Vx≤ (round to 2 decimal places)
To maximize the volume of the newly created box, how much should be cut from each corner?
x=x= inches
What is the maximum volume the box can hold?
V=V= in3
What is the largest cutsize you can cut out of the paper and still create a box with volume 130in3130in3?
x=x=
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