Question

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?

Answer 1

The length is no more than 56 inches.

The volume of the box is 8064 cubic inches.

Explanation:

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,

`P=4* s`

`P=4* 12`

`P=48`

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,
`L+48\leq 104`

`L\leq 56`

The length is no more than 56 inches.

The maximum volume of such a box would be,

`V=L* B`

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

So,
`B=12^2=144`

The volume is

`V=56* 144`

`V=8064\ in^3`

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