# Find dimensions of box

• Mar 29th 2010, 01:00 AM
womatama
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
• Mar 29th 2010, 01:10 AM
mathemagister
Quote:

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.