Linear Law

A pyramid-shaped container has a rectangular base. The length of the base is \(x\) cm, and the width is \((px + q)\) cm, where \(p\) and \(q\) are unknown constants. The height of the pyramid is also \(x\) cm.

1. Write an expression for the volume, \(V\) \(\text{cm}^3\), of the container in terms of \(x\).
2. The table below shows corresponding values of \(x\) and the volume \(V\):

   \(x\)(cm)	\(5\)	\(10\)	\(15\)	\(20\)
   \(V\)(cm\(^{3}\))	\(106\)	\(600\)	\(1650\)	\(3600\)

   1. Define suitable variables and plot a straight line graph on graph paper.
   2. Use your graph to estimate the values of \(p\) and \(q\).
3. By drawing an additional straight line on your graph from part (b), estimate the value of \(x\) and the corresponding value of \(V\) if the container is a cube.