Parameterizing Surfaces - Exercises Worksheet by Mike May, S.J. - maymk@slu.edu Revised by Russell Blyth - blythrd@slu.edu restart: Doing lots of 3D plots can cause memory problems. To avoid computer crashes we have split the exercises from the remainder of the worksheet. Exercises 1. Run (and print, if you wish) the worksheet on parameterizing surfaces. After working through that worksheet, quit Maple and restart this worksheet. 2. Use Maple to graph the parametric surfaces described below. Add a description of each surface in words. (a) x=5*cos(t), y=5*sin(t), z=7, 0 \342\211\244 t \342\211\244 2*Pi (b) x=5*cos(t), y=5*sin(t), z=5*t, 0 \342\211\244 t \342\211\244 2*Pi (c) x=2*z*cos(t), y=2*z*sin(t), z=z, 0 \342\211\244 t \342\211\244 2*Pi, 0 \342\211\244 z \342\211\244 7 (d) x=x, y=x^2, z=z, -5 \342\211\245 x \342\211\244 5, 0 \342\211\244 z \342\211\244 7 (e) x= cos(s-t), y = sin(s-t), z = s+t, 0 \342\211\244 s \342\211\244 10, 0 \342\211\244 t \342\211\244 10 3. Using parametric equations, graph the surfaces described below. Add a description of the surface in words. (a) A sphere centered at the origin with radius 5. (b) A sphere centered at (2, -1, 3) with radius 5. (c) The cone with x^2 + x^2 = z^2 with z \342\211\244 10 (d) The vase formed by rotating the curve z = 10*sqrt(x-1), 1 \342\211\244 x \342\211\244 2 around the z-axis. 4. The surface S is a deformed torus. The radial cross section is an ellipse of height 2 + sin(theta) and of width 3 + cos(2*theta), centered 6 + sin(3*theta) from the z-axis. Parameterize S and graph it.