a shipping box is shaped like a rectangular prism.it has a total volume of 96 cubic inches. the height is two inches less than the width. what are the dimensions of the box?
Volume = product of three dimensions.
What is the relation of the third dimension to either of the other two?
Let's assume the width of the shipping box is "W" inches.
According to the given information, the height of the box is two inches less than the width, so the height would be (W - 2) inches.
Since it is a rectangular prism, the volume of the box can be calculated by multiplying the length, width, and height:
Volume = Length × Width × Height
Given that the total volume of the box is 96 cubic inches, we can write the equation as:
96 = Length × W × (W - 2)
To find the dimensions, we need to solve this equation. However, we don't have any additional information about the length, so we cannot determine an exact solution.
To find the dimensions of the box, we need to set up and solve an equation based on the given information.
Let's assume:
Width = W inches
Height = W - 2 inches
Length = L inches
The volume of a rectangular prism is calculated by multiplying its length, width, and height. Therefore, we can write the equation:
Volume = Length × Width × Height
Given that the total volume of the box is 96 cubic inches:
96 = L × W × (W - 2)
Now we have an equation with two variables, W and L. We need to find their values.
Simplifying the equation:
96 = L × (W^2 - 2W)
Distributing L across the terms:
96 = L × W^2 - 2L × W
Since we cannot solve this equation without having the value of L, we need additional information to find the dimensions of the box. Could you provide any further information or constraints?