(Solved): Classwork 1) Use Pappus' theorem to derive the formula for the volume of a cone as follows: a) Dra ...

Classwork 1) Use Pappus' theorem to derive the formula for the volume of a cone as follows: a) Draw a triangle with vertices at $(0,0),(r,0)$, and $(0,h)$ b) Find the $x$ coordinate of the centroid of the triangle (Hint: the centroid of the triangle would have the same coordinates as the center of mass of the system of particles of equal mass that are located at the vertices .) c) Apply Pappus' theorem to get the volume of the cone formed when this region is rotated about the $y$-axis. 2) Find parametric equations for the line segment going from $P(?4,1)$ to $Q(3,3)$. 3) a) Sketch and label the arc of the ellipse, centered at the origin, going from the point $(0,1)$ (at $t=0)$ counterclockwise to the point $(3,0)$ (at $t=?/2)$. b) Find parametric equations for this curve.