A postal service requires that any box sent by priority mail have length plus girth (distance around) totaling no more than 104 in. One volume that meets this condition is contained by a box with a square end 12 in. on each side. What is the length of the box? What is the volume?

Given : A postal service requires that any box sent by priority mail have length plus girth (distance around) totaling no more than 104 in. One volume that meets this condition is contained by a box with a square end 12 in. on each side.

To find : What is the length of the box? What is the volume?

Solution :

A square end 12 inch on each side.

Then the girth of the box is given by,

[tex]P=4\times s[/tex]

[tex]P=4\times 12[/tex]

[tex]P=48[/tex]

The girth of the box is 48 inches.

A postal service requires that any box sent by priority mail have length plus girth (distance around) totaling no more than 104 in.

So, [tex]L+48\leq 104[/tex]

[tex]L\leq 56[/tex]

The length is no more than 56 inches.

The maximum volume of such a box would be,

[tex]V=L\times B[/tex]

B = area of the base (or end) of the box,

So, [tex]B=12^2=144[/tex]

The volume is

[tex]V=56\times 144[/tex]

[tex]V=8064\ in^3[/tex]

Therefore, The volume of the box is 8064 cubic inches.

A postal service requires that any box sent by priority mail have length plus girth​ (distance around) totaling no more than 104 in. One volume that meets this condition is contained by a box with a square end 12 in. on each side. What is the length of the​ box? What is the​ volume?

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A postal service requires that any box sent by priority mail have length plus girth (distance around) totaling no more than 104 in. One volume that meets this condition is contained by a box with a square end 12 in. on each side. What is the length of the box? What is the volume?