CAMBBIA STEEL. 



499 



AREAS AND CIRCUMFERENCES OF CIRCLES. 



(CONCLUDED.) 



To find from the table areas or circumferences for larger diameters than those 

 given. 



CASE I. 



For diameters greater than 100 and less than 1001: 



Take from the table the area or circumference for a circle the diameter of 

 which is one-tenth of the given diameter. 



To obtain the required area or circumference, multiply the area so found by 

 100 and the circumference so found by 10. 



For Example. What is the area and circumference corresponding to a 

 diameter of 459? 



From the tables the area and circumference for diameter 45.9 are 1 654.6847 

 and 144.1991. Therefore 165 468.47 and 1 441.991 are the area and circum- 

 ference required. 



CASE II. 



For diameters greater than 1000: 



Divide the given diameter by any convenient factor which will give as a 

 quotient a diameter found in the table, and take from the table the area or 

 circumference for this diameter. 



To obtain the required area or circumference multiply the area so found by 

 the square of the factor and the circumference so found by the factor. 



For Example. What is the area and circumference corresponding to a 

 diameter of 1 983? 



1 983 -J- 3 = 661. From the tables and Case I the area and circumference 

 for diameter 661 are 343 156.95 and 2 076.593. Therefore 343 156.95 X 9 = 

 3 088 412.55 = area required, and 2 076.593 X 3 = 6 229.779 = circumference 

 required. 



