Square piece of material, 24 cm on a side, by cutting equal squares fr

1.	Square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Express the volume V of the box as a function of x.
Answer» 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

Square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Express the volume V of the box as a function of x.

Answer»

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