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Answer:
of square should be cut out of each corner to create a box with the largest volume.
Step-by-step explanation:
Given: Dimension of cardboard= 16 x 30“.
As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.
Lets assume the cut out size of each corner be "x".
∴ Size of cardboard after 4 corner will be cut out is:
Length (l)=
Width (w)=
Height (h)=
Now, finding the volume of box after 4 corner been cut out.
Formula; Volume (v)=
Volume(v)=
Using distributive property of multiplication
⇒ Volume(v)=
Next using differentiative method to find box largest volume, we will have
Differentiating the value
⇒
taking out 12 as common in the equation and subtituting the value.
⇒
solving quadratic equation inside the parenthesis.
⇒=0
Dividing 12 on both side
⇒= 0
We can again take common as (x-12).
⇒ =0
∴
We have two value for x, which is
12 is invalid as, w=
∴ 24 inches can not be cut out of 16 inches width.
Hence, the cut out size from cardboard is
Now, subtituting the value of x to find volume of the box.
Volume(v)=
⇒ Volume(v)=
⇒ Volume(v)=
∴ Volume(v)= 725.93 inches³