Final answer:
To find the dimensions of the pyramid-shaped paperweight with a given volume of 12 cubic inches, you need to solve for the length using the formula for the volume of a rectangular pyramid, and from there, calculate the width and height as they are defined relative to the length.
Step-by-step explanation:
The student's question requires solving for the dimensions of a pyramid-shaped paperweight given its volume and the relationship between its length, width, and height. Since the paper company team has decided that the width of the paperweight is 4 inches less than the length (L) and the height of the paperweight is 3 inches less than the length, we can represent the width as (L - 4) inches and the height as (L - 3) inches. The volume of a rectangular pyramid is given by the formula V = (1/3) x length x width x height.
Given the volume (V) is 12 cubic inches, we can set up the equation:
12 = (1/3) x L x (L - 4) x (L - 3)
By solving this equation, we find the dimensions that satisfy the volume requirement for the paperweight.