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

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

Answer 2

Answer:

The dimension of the rectangle is $16\times 17\times 18$

Step-by-step 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

$V=l\times b\times h$

$4896=x\times (x+1)\times (x+2)$

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

$4896=x^3+2x^2+x^2+2x$

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

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 $16\times 17\times 18$