Question

A suitcase has a length that is 10 inches greater than its width. The sum of the length, width and height of the suitcase is 40 inches. Write a polynomial expression to represent V, the volume of a rectangular prism. (Volume = (length)(width)(height

Answer 1

Start with what we know.... sum of length width and height = 40
\[(10+w) + w + h = 40 => h = 30-2w\]
Volume is area of the base times the height so we get
Area of base x height = \[(10+w)*w*h = hw^2 + 10hw = Volume\]
Now substitute in the expression for h we get
\[-2w^3 + 10w^2 + 300w = Volume\]
As a test, let w = 10, length = w+10=20, height = 40-30= 10
So multiple these together to get volume = 10*20*10 = 2000
Set w = 10 in our equation
\[-2(10)^3 + 10(10)^2 + 300(10) = 2000\]