Let C be the curve x = f(t), y = g(t), for a stsb, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], the area of the b surface obtained by revolving C about the x-axis is S = [2r g(t) √/f'(t)² + g' (t)² dt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is a b S= = [2n f(t) √ 1 (t)² + g' (t)² dt. a Consider the curve x = 3cos (t), y = 3sin (t) + 6 on 0 st≤ 2. Complete parts (a) and (b) below. a. Describe the curve. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) OA. A circle of radius OB. A sphere of radius OC. An ellipse of horizontal radius and vertical radius OD. A line that rises from left to right with a y-intercept of b. If the curve is revolved about the x-axis, describe the shape of the surface of revolution and find the area of the surface. Start by describing the revolved shape. O A torus (doughnut) O A cylinder O A circle OA sphere O An ellipse centered at centered at .... centered at

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