# Thread: Find dimensions of box

1. ## Find dimensions of box

When the edges of a cuboid-shaped box are increased by 2cm, 4cm and 5cm respectively, it would become a cube.
The volume would increase by $\displaystyle 440cm^3$
Find the dimensions of the original cuboid-shaped box.

I found that the dimensions are 6cmx4cmx3cm by fluke so can anyone please explain how to solve it?
TY

2. Originally Posted by womatama
When the edges of a cuboid-shaped box are increased by 2cm, 4cm and 5cm respectively, it would become a cube.
The volume would increase by $\displaystyle 400cm^3$
Find the dimensions of the original cuboid-shaped box.

I found that the dimensions are 6cmx4cmx3cm by fluke so can anyone please explain how to solve it?
TY
You get solvable simultaneous equations.

Just translating the above information into Math:

$\displaystyle V=xyz$ (the definition of the volume of a cuboid)

$\displaystyle V+400 = (x+2)(y+4)(z+5)$ (the changes you said)

$\displaystyle x+2=y+4=z+5$ (since these would make the sides of a cube, which are always equal)

Now simply solve.

Hope that helps

Mathemagister

PS If you need help with solving that, feel free to ask.