Area Problem: The areas of similarly shaped objects are directly proportional to the

Chapter 7, Problem 26

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Area Problem: The areas of similarly shaped objects are directly proportional to the square of a linear dimension. a. Give the formula for the area of a circle. Explain why the area varies directly with the square of the radius. b. If a grapefruit has twice the diameter of an orange, how do the areas of their rinds compare? c. When Gutzon Borglum designed the reliefs he carved into Mount Rushmore in South Dakota, he started with models the lengths of the actual reliefs. How does the area of each model compare to the area of each of the final reliefs? Explain why a relatively small decrease in the linear dimension results in a relatively large decrease in the surface areas to be carved. d. Gulliver traveled to Brobdingnag, where people were 10 times as tall as normal people. If Gulliver had 2 m2 of skin, how much skin surface would you expect a Brobdingnagian to have had?