Question

An open box is to be made from a square piece of material, 24 cm on a side, by

cutting equal squares from the corners and turning up the sides.

Express the volume V of the box as a function of x. ​

Answer 1

Answer:

The volume of the box expressed as a function of x will be

V = 4x³ - 96x² + 576x

Step-by-step explanation:

Initial length of the square piece = 24

After cutting x cm from each corner, the remaining dimension of the box can be given as below:

Length of the box = 24-2x

breadth of the box = 24 - 2x

height of the box = x

we know that the volume of a cuboid is given as,

V = L * B * H

= (24-2x)(24-2x)x

= x(24-2x)²

= x( 576 + 4x² - 96x)

=> V = 4x³ - 96x² + 576x

Which is the required volume of the box expressed as a function of x.