The closed rectangular box has side lengths 2n-2, 2n+2, and 2n inches.

Question

Write a polynomial function V (n) for the volume of the box.

What is the volume when the length is the shortest side is 4 inches.

Write a polynomial function A (n) for the area of the base of the box.

Answer 1

The volume can be written as: V(n) = 2n(2n-2)(2n+2) = 2n (4n² - 4) = 8n³ - 8n.

The length of shortest side is 2n-2 = 4, therefore n =3. So the volume will be V(3) = 192.

The A(n) = (2n-2) (2n+2) = (4n² - 4) .