need help asappp

[amra55]

Denise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construct a larger box in the shape of a cube with a volume of 2,000 cubic inches. By how many inches, to the nearest tenth, should she increase the length of each side of the original box?

 

[Denis]

What is the volume of the original box?

 

[Mrspi]

Denise is designing a storage box in the shape of a cube. Each side of the box has a length of 10 inches. She needs more room and decides to construct a larger box in the shape of a cube with a volume of 2,000 cubic inches. By how many inches, to the nearest tenth, should she increase the length of each side of the original box?

I think we've seen this question here before!

For a rectangular solid (in general),

volume = length * width * height

In the case of a cube, the length, the width, and the height are all the same....let's call each of those "s"

For a cube, then,

volume = s * s * s

or,

volume = s[sup:27oxxi08]3[/sup:27oxxi08]

Now...when the length of one side is 10 in,
volume = (10 in)[sup:27oxxi08]3[/sup:27oxxi08]

You want to add a certain amount to each side to increase the volume to 2000 in[sup:27oxxi08]3[/sup:27oxxi08]. Let x = the number of inches you add

the new volume will be

V = (10 + x)[sup:27oxxi08]3[/sup:27oxxi08]

And you want the new volume to be 2000 in[sup:27oxxi08]3[/sup:27oxxi08]

So....

2000 = (10 + x)[sup:27oxxi08]3[/sup:27oxxi08]

 

[amra55]

thank you so much!