CYLINDER 



1681 CYNIC SCHOOL OF PHILOSOPHY 



radius and 10 inches high. The solution fol- 

 lows: 



Circumference of a circle = 2x 3. 1416 X radius. 



Circumference of can in sq. in. = 2 X 3. 1416 X3 = 

 18.8496. 



Lateral surface in sq. in.= 10 X 18.8496 = 

 188.496. 



How many square inches of tin will be re- 

 quired for the entire can? The bases are 

 circles; therefore the area of each base equals 

 3.1416Xradius 2 (see CIRCLE). 



Area of 2 bases in sq. in.= (3.1416 X3 2 ) X2 = 

 56.5488. 



Lateral surface in sq. in. = 188.496. 



Entire surface in sq. in. = 245. 0448 (sum of 

 56.5488 and 188.496). 



The volume of a cylinder equals the product 

 of the area of one base and the altitude ; ex- 

 pressed more concisely: 



Volume of cylinder=3.1416X radius 2 X alti- 

 tude. 



The number of cubic inches in the above can 

 is found as follows: 



Radius = 3 in. 

 Altitude^: 10 in. 

 Volume in cu. in. = 3.1416X3 2 XlO = 282.744. 



Practical Problems. A well is 30 feet deep 

 and 4 feet in diameter. How many gallons of 

 water will it hold? 



We see that the well is a cylinder. The base 

 is a circle whose radius is 2 feet, and the depth 

 of well, 30 feet, is the altitude of the cylinder. 

 The solution is as follows: 



Area of base in sq. ft. = 3.1416x2 2 =12.5664. 



Volume in cu. ft.= 12. 5664 X 30 = 376. 992. 



1 cu. ft. = 1728 cu. in. 



376.992 cu. ft. = 376. 992 X 1728 cu. in. = 651442.- 

 175 cu. in. 



231 cu. in. = l gallon. 



Number gal. in well = 651442. 176^231 = 2830.- 

 096. 



The solution may be shortened as below by 

 cancellation : 



Radius = 2 ft. 



Area of base in sq. ft. = 3. 1416 X2 2 =12. 5664. 



Volume in cu. ft. = 12. 5664X30 = 376.992. 



231 cu. in. = l gallon. 



1728 cu. in. = l ft. 



4.896 

 -34s2f2 576 



Number gallons in well =^^^^i^ = 2820.096 



5? 



-7- 



How many square inches are there in the 

 lateral surface of a lead pencil which is one- 

 fourth inch in diameter and six inches long? 



Take a piece of paper \\V-i inches wide and 

 20 inches long. Roll it to form a cylinder, 

 us-ing the % inch from ll l /2 inches to paste as 

 106 



a lap. What is the circumference of the cylin- 

 der? Find its diameter and radius. 



The circumference = 3. 1416 X diameter. There- 

 fore 11 = 3.141 6 X diameter. (For many practical 

 problems we may use 3V? instead of 3.1416.) Do 

 so here and see that 11 = 3^ X diameter ; diameter 



2 



Find the area of the ends of your cylinder. 

 Solution as follows: 



Area of a circle = 3 VrX radius 2 . . 

 Area of 2 bases = 3#X (1% ) Z X2 = 



11 7 



Area of bases = 19Vi sq. in. 



Second solution: We may use the fact that 



Area= ra IUS x circumference. 



A 



Area of 1 base = ^Xll=jX^Xll=9| 

 2 42 8 



Area of 2 bases = 2 X 9% = 19^4. 

 Area of bases=19}4 sq. in. 



How many cubic feet of water can be stored 

 in a cylindrical reservoir 40 feet in radius 

 and 60 feet high? 



The volume of the cylinder is a problem 

 which enters largely into the industrial world; 

 for example, in the building of reservoirs, pipes 

 and tanks for transporting oils, and in the con- 

 struction of engines and machines of various 

 kinds, a knowledge of the capacity of the 

 cylinder is essential. A.H. 



CYNIC, sin'ik, SCHOOL OF PHILOSOPHY, 

 . a system of Greek philosophy founded in 

 the fourth century B. c. by Antisthenes, a disci- 

 ple of Socrates. He took as his starting point 

 the doctrine of his great teacher, that virtue 

 and not pleasure is the chief end of life, and 

 it alone constitutes true happiness. From this 

 he argued that since continued happiness is not 

 possible if man has wants and desires which 

 may not be satisfied, virtue consists in living 

 as much as possible unfettered by desires. 

 Therefore, the wise man is the one who looks 

 with indifference on all the ordinary pleasures 

 of life and who lives for and in himself alone. 



Among the enthusiastic followers of Antis- 

 thenes was Diogenes (which see), who carried 

 the principles of the school to an extreme, liv- 

 ing, it is said, on the coarsest bread and sleep- 

 ing at night in a tub. Zeno and Demetrius, 

 the latter of the later Roman period, were 

 other distinguished Cynics. Though not of 

 the greatest importance as a school of philoso- 

 phers, the Cynics form the link between Soc- 



