Question

Write an expression that represents the volume of a rectangular-shaped box with a length 3 inches less than its height and a width 4 inches greater than its height.

A. x^3 + x^2 – 12x
B. x^2 + x – 12
C. x^2 – 7x + 12
D. 4x^3 – 3x^2 – 12

1. The expression that represents the volume of a rectangular-shaped box is: A. x³ + x² – 12x.

### What is the Volume of a Rectangular Prism?

A rectangular-shaped box is a rectangular prism. To find the volume of a rectangular-shaped box, we would apply the formula of the volume of a rectangular prism, which is expressed as: V = (length)(width)(height).
We are given the following dimensions of the rectangular-shaped box:
Let the height be represented as x
Height of the rectangular-shaped box = x in.
Length of the rectangular-shaped box = (x – 3) in.
Width of the rectangular-shaped box = (x + 4) in.
Plug in the values into the volume formula:
Volume of the rectangular-shaped box = (x – 3)(x)(x + 4)
Expand (x – 3)(x)(x + 4)
Volume of the rectangular-shaped box = x³ + x² – 12x.
Therefore, the expression that represents the volume of a rectangular-shaped box with the given dimensions is: A. x³ + x² – 12x.