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

Answer:

The length is no more than 56 inches.

The volume of the box is 8064 cubic inches.

Step-by-step 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,

$P=4\times s$

$P=4\times 12$

$P=48$

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,

$V=L\times B$

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

So, $B=12^2=144$

The volume is

$V=56\times 144$

$V=8064\ in^3$

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