20. (Total Score: 14 points) Subproblem 1: 7 points, Subproblem 2: 7 points. As shown in the figure, to make a cylindrical lantern, 4 congruent rectangular frames are first made, using a total of 9.6 meters of wire. Then $S$ square meters of plastic sheet is used to form the lateral surface and bottom of the cylinder (the top is not installed). [Figure] (1) For what value of the cylinder's base radius $r$ does $S$ attain its maximum value? Find this maximum value (result accurate to 0.01 square meters); (2) To make a lantern as shown with base radius 0.3 meters, draw the three-view drawing for making the lantern (when drawing, structural factors such as frames need not be considered).
(10 points) Let $F _ { 1 } , F _ { 2 }$ be the left and right foci of the ellipse $E :
20. (Total Score: 14 points) Subproblem 1: 7 points, Subproblem 2: 7 points.
As shown in the figure, to make a cylindrical lantern, 4 congruent rectangular frames are first made, using a total of 9.6 meters of wire. Then $S$ square meters of plastic sheet is used to form the lateral surface and bottom of the cylinder (the top is not installed).\\
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(1) For what value of the cylinder's base radius $r$ does $S$ attain its maximum value? Find this maximum value (result accurate to 0.01 square meters);\\
(2) To make a lantern as shown with base radius 0.3 meters, draw the three-view drawing for making the lantern (when drawing, structural factors such as frames need not be considered).