Question

Ansh wants to make a box. He starts with a piece of cardboard whose length is
18cm and width is 12cm. He cuts 4 equal square with sides of 4cm at the four
corners and folded at the broken lines to make a box. The volume of the box is________.
​

Answer 1

Step-by-step explanation:

a)

The volume of the box is:

V=lwh

V=lwh

Since l=12−2xl=12−2x, w=12−2xw=12−2x, and h=xh=x, the volume is:

V(x)=(12−2x)(12−2x)(x)

V(x)=(12−2x)(12−2x)(x)

V(x)=(144−48x+4x2)(x)

V(x)=(144−48x+4x

2

)(x)

V(x)=144x−48x2+4x3

V(x)=144x−48x

2

+4x

3

or

V(x)=4x3−48x2+144x

V(x)=4x

3

−48x

2

+144x

b)

Each dimension of the box must be greater than 0 so:

12−2x>0→x<6

12−2x>0→x<6

12−2x>0→x<6

12−2x>0→x<6

x>0

x>0

So, the domain is:

0<x<6

0<x<6