ANSWER and EXPLANATION
We want to order the functions from widest to narrowest:
![\begin{gathered} y=3x^2 \\ y=2x^2 \\ y=4x^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D3x%5E2%20%5C%5C%20y%3D2x%5E2%20%5C%5C%20y%3D4x%5E2%20%5Cend%7Bgathered%7D)
To do this, we have to plot the graphs of the functions by using a table of values.
Let us find the values of the functions for values of x = -2, 0, 2
For the first function:
![\begin{gathered} y=3x^2 \\ \Rightarrow x=-2: \\ y=3(-2)^2=3*4 \\ y=12 \\ \Rightarrow x=0: \\ y=3(0)^2=3*0 \\ y=0 \\ \Rightarrow x=2: \\ y=3(2)^2=3*4 \\ y=12 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D3x%5E2%20%5C%5C%20%5CRightarrow%20x%3D-2%3A%20%5C%5C%20y%3D3%28-2%29%5E2%3D3%2A4%20%5C%5C%20y%3D12%20%5C%5C%20%5CRightarrow%20x%3D0%3A%20%5C%5C%20y%3D3%280%29%5E2%3D3%2A0%20%5C%5C%20y%3D0%20%5C%5C%20%5CRightarrow%20x%3D2%3A%20%5C%5C%20y%3D3%282%29%5E2%3D3%2A4%20%5C%5C%20y%3D12%20%5Cend%7Bgathered%7D)
Hence, its table is:
For the second function:
![\begin{gathered} y=2x^2 \\ \Rightarrow x=-2: \\ y=2(-2)^2=2*4 \\ y=8 \\ \Rightarrow x=0: \\ y=2(0)^2=2*0 \\ y=0 \\ \Rightarrow x=2: \\ y=2(2)^2=2*4 \\ y=8 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D2x%5E2%20%5C%5C%20%5CRightarrow%20x%3D-2%3A%20%5C%5C%20y%3D2%28-2%29%5E2%3D2%2A4%20%5C%5C%20y%3D8%20%5C%5C%20%5CRightarrow%20x%3D0%3A%20%5C%5C%20y%3D2%280%29%5E2%3D2%2A0%20%5C%5C%20y%3D0%20%5C%5C%20%5CRightarrow%20x%3D2%3A%20%5C%5C%20y%3D2%282%29%5E2%3D2%2A4%20%5C%5C%20y%3D8%20%5Cend%7Bgathered%7D)
Hence, its table is:
For the third function:
![\begin{gathered} y=4x^2 \\ \Rightarrow x=-2: \\ y=4\left(-2\right)^2=4*4 \\ y=16 \\ \Rightarrow x=0: \\ y=4(0)^2=4*0 \\ y=0 \\ \Rightarrow x=2: \\ y=4(2)^2=4*4 \\ y=16 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20y%3D4x%5E2%20%5C%5C%20%5CRightarrow%20x%3D-2%3A%20%5C%5C%20y%3D4%5Cleft%28-2%5Cright%29%5E2%3D4%2A4%20%5C%5C%20y%3D16%20%5C%5C%20%5CRightarrow%20x%3D0%3A%20%5C%5C%20y%3D4%280%29%5E2%3D4%2A0%20%5C%5C%20y%3D0%20%5C%5C%20%5CRightarrow%20x%3D2%3A%20%5C%5C%20y%3D4%282%29%5E2%3D4%2A4%20%5C%5C%20y%3D16%20%5Cend%7Bgathered%7D)
Hence, its table is:
Now, let us plot the graphs of the functions:
Therefore, from the graph, we see that the order of the functions from widest to narrowest is:
93/4
9/4=2r1
13/4=4r1
10/4=2r2
20/5=4
=23.25
The area of the rectangle would be 45 m^3