1. ## Word problem

A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and$6.00 per square meter for the sides. What is the cost for the box?

Thanks

2. Originally Posted by roseh
A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and$6.00 per square meter for the sides. What is the cost for the box?

Thanks
The width of the box is $4$m, let the height be $h$m and the depth be $d$m.

Then to make the volume $64 m^3$ we have:

$
4\times h \times d=64
$

The area of the base is $4\times d$ so the cost of the base is:

$
6 \times 4 \times d
$

The area of the sides id $(2 \times 4+2\times d)\times h$, so the cost of the sides is:

$
12 \times (2 \times 4+2\times d)\times h =96+24\times d \times h
$

but $4\times h \times d=64$, so the cost of the sides is:

$
96+24\times d \times h=96+6 \times (4 \times d \times h)=\ 480
$
.

Hence the total cost is:

$
480+24 \times d
$
dollars

and you don't know enough to simplify further.

RonL