The volume of the box is the amount of space in it.
The dimension of the postcard is:
Let x represents the length of the cut.
So, the dimension of the box is:
<u>(a) The function that represents the volume of the box</u>
This is calculated as:
So, we have:
Expand
Hence, the volume function is:
<u>(b) The dimension that maximizes the volume</u>
We have:
Differentiate
Set to 0
Using a calculator, we have:
The value x = 7.3 is greater than the dimension of the box.
So, we have:
Recall that:
So, we have:
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
<u>(c) The maximum volume</u>
This is calculated as the product of the dimension of the box
So, we have:
Hence, the maximum volume of the box is 168.1 cubic inches
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