Session 9:
Homework

 Problem H1 Reptiles need the sun to get them going. Many large dinosaurs had to have large fins or plates down their back. How does this fact relate to what you have learned about the proportion of surface area to volume?

Problem H2

A manufacturer is producing half-liter aluminum cans in a cylindrical shape. The volume of the can is 500 cm3.

 a. Find the radius and height for the can that will use the least aluminum and therefore be the cheapest to manufacture. In other words, minimize the surface area of the can. b. What shape is your can? Do you know of any cans that are made in this shape? Can you think of any practical reasons why more cans are not made in this shape?

 Problem H3 Some aspirin-like tablets are said to work "two and a half times faster" than their competitors. What is an obvious way in which this could be accomplished?

 Problem H4 Mr. Hobbs had an ugly blob in the middle of his wall. The paint on the rest of the wall looked fresh, so Mr. Hobbs asked the painter to come and paint only the blob. The painter said he would charge according to the area that needed to be painted. To figure out how much the job would cost, Mr. Hobbs ran a string around the edge of the blob so that it covered the border perfectly. Then, to figure out the area, he removed the string, shaped it into a rectangle, and figured out the area of the rectangle. How close did Mr. Hobbs's estimate come to the painter's bill for painting the blob?

 Problem H5 In cubes, you found a proportional relationship between volume and surface area. Does the proportional relationship between volume and surface area also exist for spheres?

 The volume of a sphere is (4/3)r3, and the surface area of a sphere is 4r2.   Close Tip The volume of a sphere is 4/3r3, and the surface area of a sphere is 4r2.

 Problem H2 adapted from Swan, Malcolm, and the Shell Centre Team. The Language of Functions and Graphs. p. 174. © 1999 by Shell Centre Publications. http:// www.MathShell.com. Problem H4 adapted from Lamon, Susan J. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers. © 1999 by Lawrence Erlbaum Associates.
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