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Whether wallpapering a footlocker or filling a cylinder with corncobs, a knowledge of three-dimensional shapes is essential. This program demystifies the subjects of surface area and volume by sharing solid information backed up by the surface area formulas for right cylinders and spheres and the volume formulas for right prisms, cylinders, and spheres. “Surface Area and Volume.” Films Media Group, 1999, fod.infobase.com/PortalPlaylists.aspx?wID=97832&xtid=10233. Accessed 10 June 2019.
In this program submarines, evolution, and telescopes are all part of a discussion of rational functions. In the first segment, functions are used to calculate how much water pressure a submarine can withstand before it implodes. Studying the ratio of surface area to volume of both a snake and a polar bear in the second segment yields clues about how animals have adapted to their environment. Finally, the inner workings of the Hubble space telescope are explained in terms of rational functions. “Rational Functions.” Films Media Group, 2011, fod.infobase.com/PortalPlaylists.aspx?wID=97832&xtid=44714. Accessed 10 June 2019.
Contents: Volume and Density (1:53) -- Geometry of Density (2:01) -- Density Exploration on TI-Nspire (3:30) -- Hull of Titanic: Triangular Prism (2:08) -- Density and the Hull of the Titanic (3:33) -- Calculations: Sinking of the Titanic (2:40) -- Surface Area of Pyramids (3:26) -- Isosceles Triangle on TI-Nspire (3:35) -- Length and Height of Pyramid (1:33) -- TI-Nspire Concepts (2:05) -- Construction of Rhombus Shape (2:56) -- Surface Area of Glass Pyramid (1:45) -- Surface Area to Volume Ratio (2:29) -- Shape Determination (0:55) -- TI-Nspire Exploration (2:14) -- Energy Efficiency of Tall Buildings (1:35) -- Credits: Area and Volume (0:10)
To develop an understanding of direct vatiation, in Part I, Peggy Lynnѫs students simulate oil spills on land and investigate the relationship between the volume and the area of the spill. In Part II, they develop the concept of inverse variation by examining the relationship of the depth and surface area of a constant volume of water that is transferred to cylinders of different sizes. Annenberg/CPB, 2004.
Provides examples of special functions in the form of direct variation and inverse variation, with a discussion of combined variation and the constant of proportionality. These concepts are explored in relation to polynomials and assorted equations, with applications from chemistry, physics, astronomy, and the food industry. Annenberg /CPB, 1991.