# A box without a lid is to be made from a sheet of thin metal. The sheet measures 20 cm by 20 cm. squares of side x cm are cut from each corner and the sides folded up. What is the formula for the volume?

Formula for volume is $x {\left(20 - x\right)}^{2}$ or ${x}^{3} - 40 {x}^{2} + 400 x$ $c u c m$.
As we are cutting squares of side $x$ cm, the height of cuboid is $x$.
Length and width will be $\left(20 - 2 x\right)$ each, as we are cutting from a square sheet.
Hence volume will be $x {\left(20 - x\right)}^{2}$ or ${x}^{3} - 40 {x}^{2} + 400 x$ $c u c m$.