Question

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)

Answer 1

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

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