Question

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x

Answer 1

After cutting squares we will get a cuboid,

length of the cuboid (l) = 24 – 2x

breadth of the cuboid (b) = 24 – 2x

height of the cuboid (h) = 2x

Volume of the box = Volume of the cuboid

V = (24 – 2x)(24 – 2x) (x)

= (24 – 2x)² (x)

= (576 + 4x² – 96x) x

= 576x + 4x³ – 96x²

V = 4x³ – 96x² + 576x

V(x) = 4x³ – 96x² + 576x