a square piece of cardboard is to be formed into a box to transport pizzas. The box is formed by cutting 2-inch squares corners from the cardboard and folding them up. If the volume of the box is 512 in^3, what are the dimensions of the cardboard? Is this a volume or area problem?

Question

a square piece of cardboard is to be formed into a box to transport pizzas.  The box is formed by cutting 2-inch squares corners from the cardboard and folding them up.  If the volume of the box is 512 in^3, what are the dimensions of the cardboard?  Is this a volume or area problem?

amistre64 · Answer

$$V_{box}=height*width*length$$

amistre64 · Answer

since its a square; the width and length are the same

amistre64 · Answer

the problem is an area problem

amistre64 · Answer

512 = 2(side-2)^2

512/2 = (side-2)^2

sqrt(512/2) = side-2

2 + sqrt(512/2) = side

amistre64 · Answer

that comes to each side was originally 18 inches before being cut out

amistre64 · Answer

but i gotta wonder just how an open box transports pizzas

anonymous · Answer

so add the 2-inch for the corners that are folded up make the dimensions 20 x 20

anonymous · Answer

very good question  :)

amistre64 · Answer

no; the equation factors that 2 inches in to get  18 inches for a starting value

anonymous · Answer

so 18 x 18 dimensions

amistre64 · Answer

to dbl chk; 18-2 = 16

16^2 = 256

256*2 = something close to 512 :)

amistre64 · Answer

that dont compute right does it...

amistre64 · Answer

it should be 4 inches from each side; 2 from each corner

anonymous · Answer

yes bc it's a square so 2 x 2=4

amistre64 · Answer

512 = 2(side-4)^2 
512/2 = (side-4)^2 
sqrt(512/2) = side-4 

4 + sqrt(512/2) = side

amistre64 · Answer

whaddayaknow; that makes it 20 per side lol

anonymous · Answer

lol....ty

amistre64 · Answer

yw :)