Sphere and Torus


Activity A. Create a Sphere


Activity B. Create a Hemisphere

BeachBall-SemiCircle-PatternPiece.jpg
Hemisphere Pattern Piece


BeachBall-SemiCircle-RotatePath.jpg
Hemisphere Rotate Path


BeachBall_HalfSphere.jpg
SketchUp Hemisphere


Activity C. Create a Torus - Model of a Pink Inner Tube

InnerTubeOne.jpg
InnerTubeTwo.jpg
InnerTubeThree.jpg
Extension - Examine the cross sections of the torus to determine symmetry
If we section the tube from the top, we see concentric circles that would not change if the solid was rotated about the blue axis (at any given degree measure). I painted the inside of the torus sky blue.
InnerTubeTopCrossSection.jpg
If we section the torus perpendicular to green-red plane, we see that the shape will change as you move horizontally across the solid. If we section the plane vertically through the blue axis, we see that the solid has an infinite number of reflection symmetries.
InnerTubeLateralCrossSection.jpg
Homework
Create the model of an inner tube that has a diameter of 50 inches. Let the diameter of the cross section be 10 inches.
PurpleInnerTube.jpg
Challenge
Put Susan in an inner tube in the water.
Susan in Pool.jpg