TABLE 4.-MULTIPLIERS FOR THE CONVERSION OF CIRCULAR LENGTHS AND AREAS. A.-Diameters B.-Circumferences C.-Radius-Lengths D.-Circumferences into Circumferences. into Diameters EXAMPLES OF THE USE OF TABLE 4. I. What is the circumference of a circle whose diameter is 113 inches? From division A of the table, we have the following: -- The answer is 355 inches; the fourth and third places of decimals being rejected as beyond the limits of exactness of the table. II. What is the radius of a circle whose circumference is 710 inches? From division D of the table, we have the following: The answer is 113 inches; the fourth place of decimals being rejected as beyond the limits of the exactness of the table. III. What is the area in square inches of a circle of 8 inches diameter? Square of 8=64 area in circular inches. Then, by division E of the table, 60......... 4....... = ...47.124 Area in square inches (to five figures only), 50-266 IV. What is the diameter of a circle whose area is 5027 square inches? From division F of the table we have Area in circular inches (to five figures only), 6400·6 the square root of which (by Table 1, the fractions being found by calculation) is 80-004, being the diameter required in inches, correct to five places of figures. V. How many radius-lengths are there in an arc of 57° 17′ 45′′? VI. How many minutes are there in the arc which is oneeightieth (or 0.0125) of a radius-length? By division K we have This table gives the circumferences and areas of circles, of diameters from 101 to 1000; the circumferences computed to two places of decimals, the areas to the nearest unit. Circumferences and areas for diameters not in the table may be computed by the aid of the following principles: 1. The circumferences of circles are proportional to their diam eters. 2. The areas of circles are proportional to the squares of their diameters. |