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Task: In this lab, we will explore how we can use integration to determine the volume of a solid obtained by rotating a region around the r or y axis. First, we discuss how to create a 3-dimensional volume out of a 2-dimensional area. Note that if we stack many 2-dimensional squares, we can obtain a 3-dimensional cube as in the picture. The volume of the cube would be the sum of all of the areas of the squares (of which there are infinitely many). We can add up infinite areas using an integral. In general, the volume of an object built from cross-sections is V = A(x) dx, where A(z) is the area of a cross-section. 1. Open the Desmos Solids of a Revolution grapher (link here). Find the menu that says Input and set f(x) = r,g(x) = 0, a = 0 and b = 9. Collapse all other menus using the D button near each menu header. Drag the Revolution slider slowly from 0 to 1. (a) What familiar shape have you made? What is the slider doing? 1 (b) The geometric formula for the volume of a cone is Vome = = arch. Compute the volume of the cone you just made.(c) Now we want to use calculus to find this same volume. i. Imagine a piece of paper positioned along the line r = c for some 0