Question

The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimensions of the bin?

Answer 1

The dimension of the rectangle is
`16* 17* 18`

Explanation:

Given : The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches.

To find : What are the dimensions of the bin?

Solution :

The dimensions of a rectangular bin are consecutive integers.

Let the consecutive integers are x,x+1,x+2

So let, length, l=x

Breadth b=x+1

Height h=x+2

The volume of the bin is

`V=l* b* h`

`4896=x* (x+1)* (x+2)`

`4896=(x^2+x)(x+2)`

`4896=x^3+2x^2+x^2+2x`

`x^3+3x^2+2x-4896=0`

Plot the equation graphically to find the value of x.

Refer the attached figure below.

The value of x is 16.

So, Length is l=16

Breadth is b=x+1=16+1=17

Height is h=x+2=16+2=18

The dimension of the rectangle is
`16* 17* 18`

Answer 2

cubed root of 4896 = 16.98

round to 17

17-1 = 16

17 +1 = 18

16* 17 *18 = 4896

bin is 16 in x 17 in x 18 in