Area by Planimeter Project: You have learned how to calculate the area of a region

Chapter 8, Problem C5

(choose chapter or problem)

Area by Planimeter Project: You have learned how to calculate the area of a region algebraically using the fundamental theorem and also numerically. There is a mechanical device called a planimeter (compensating polar planimeter) that finds the area geometrically from a drawing of the region. In this problemyou will borrow a planimeter and use it to findthe area of Brazil from a map.a. Make a copy of the map of Brazil inFigure 8-8g. Be sure to include the scalebecause some copy machines shrink thepicture.Figure 8-8gb. Set up the planimeter with the tracer pointat a convenient starting point on the map.Set the dial to zero. Then trace around theboundary until you return to the startingpoint.c. Read the final setting on the dial. Theplanimeter may have a vernier scale forreading tenths of a unit.d. Measure the scale on the map to find outhow many miles correspond to 1 cm. Beclever! Then find out how many squaremiles correspond to 1 cm2. Finally, calculatethe area of Brazil to as many significantdigits as the data justify.e. Find out from the planimeters instructionmanual the theoretical basis on which theinstrument works. Write a paragraph or twodescribing what you learned.f. Check an almanac or encyclopedia to seehow accurate your measurement is