The length, width, and height of a rectangular box are consecutive integers, and the largest dimension is k cm. find the volume V of the box

(Hint: V= lwh)

consecutive integers are integers like 1,2,3 or 3,4,5 or 101,102,103. So since the largest of the integers is k, to get the consecutive integers lower than k, you have to find the second integer which would be k-1, then the third which would be k-2.

Ohhh ok!! Thank you very much!!!

V=lwh

V=k*k-1*k-2
V=k^3-3k^2-2k

Why r we subtracting???

or if your teacher wants it in this format

V=k(k^2-3k-2)

To find the volume (V) of the rectangular box, we need to know the length (l), width (w), and height (h) of the box.

Given that the dimensions are consecutive integers and the largest dimension is k cm, we can set up the following equations:

l = k - 2 (since the length is the largest dimension minus 2)
w = k - 1 (since the width is the largest dimension minus 1)
h = k (since the height is the largest dimension)

Now, we can substitute these values into the formula for volume (V = lwh):

V = (k - 2) * (k - 1) * k
V = (k^2 - 3k + 2) * k
V = k^3 - 3k^2 + 2k

Therefore, the volume (V) of the box is k^3 - 3k^2 + 2k.