An open box is to be made from a rectangular piece of cardboard 30" x 24" by cutting equal squares from the corners and turning up the sides Write a function v (x)

v (x) = x^ (3) - 108"x^ (2) + 720"x

Step-by-step explanation:

Dimensions of rectangle,

length = 30", breadth=24"

Four equal squares are cut, at corners of rectangle.

Let the length of square cut be "x".

Thus the length of rectangle reduces to = 30" - (2x)

2a because the 2 squares are respectively cut from one corresponding length.

Similarly, the breadth of rectangle reduces to = 24" - (2x)

Thus visualizing the box formed by raising up the sides,

height = x

length = 30" - (2x)

breadth = 24" - (2x)

thus volume as function of dependent variable x is,

v (x) = (height) X (lenght) X (breadth)

= (x) X (30"-2x) X (24"-2x)

= (x) X (720"-108"x+x^ (2))

v (x) = x^ (3) - 108"x^ (2) + 720"x