Question $5.$ Consider the solid S that lies between the paraboloid z$=$x$^(2)+$y$^(2)$ and the plane z$=4.$

i$)$ Sketch this solid.

ii$)$ Determine a suitable region D over which to integrate that would allow you to calculate the volume of S$.$

iii$)$ Set up a $($sum of$)$ iterated integral$($s$)$ that, if evaluated, would give the volume

of S$.$ You may use any ideas$/$techniques discussed in $15\mathrm{.}2,$ but you must clearly indicate what you are using. You are not being asked to evaluate what you have set up$.$

iv$)$ How does the double integral $\_($D$)$x$^(2)+$y$^(2)-4$dA where D is the region you found in part $($ii$),$ relate to your answer to part $($iii$)$ and why? Hint: Draw a sketch.

You don't need to evaluate the integral.