Question

An open box can hold 80 cm3. It is made from a square piece of tinplate with 3 cm squares cut from each of its 4 corners. Find the dimensions of the original piece of tinplate.

Answer 1

Let the side of the square plate be x cm.
The height of the box is 3 cm.
The length & width are both (x-6) cm.
volume = length*width*height
=3*(x-6)*(x-6)
=80
x can then be obtained by solving
3(x-6)(x-6)=80

Answer 2

Volume of Open box which is made from square piece of tinplate=80 cm³

⇒Squares of side 3 cm is cut from 4 of it's corner.It means the square boxes are cubical.

Volume of cube=Side × Side × Side

=(Side)³

Volume of 4 cubical box having each side 3 cm

=4×3×3×3

=108 cm³

Total Volume of box=108 cm³ +80 cm³=188 cm³

Since the box is open .

Let the dimension of box be

Length= x cm

Breadth= x cm

Height = x cm

Volume of Original box=188 cm³

`\rightarrow x^3=188\\\\\rightarrow x=(188)^{(1)/(3)}\\\\x=5.728\text{approx}`

So, Original dimension of cubical Square Box=5.73 cm(Approx)