A complete and practical solution book for the common school teacher . ft. (12) SO=VIW2—KS2= (13) Area of segment KZM=(ZS3-^by twice KM) +l(ZSXKM) = sq. ft. (14) Area of triangle M0K=*(KMXSO) = sq. ft. (15) sq. ft.+ sq. sq. ft., area of sectorOKZM. (16) 427r=area of large wheel, 87r=circumference of the largewheel. (17) The arc KZM=*-42 : ::8«-: (9 05 ft.) (18) 8tt—9 05= ft = KDM, part of circumference coveredby the belt. (19) Area of the sector MLKO=42 : l2:: : ( ) (20) 27r=circumference of small wheel. (21) The arc MLK
A complete and practical solution book for the common school teacher . ft. (12) SO=VIW2—KS2= (13) Area of segment KZM=(ZS3-^by twice KM) +l(ZSXKM) = sq. ft. (14) Area of triangle M0K=*(KMXSO) = sq. ft. (15) sq. ft.+ sq. sq. ft., area of sectorOKZM. (16) 427r=area of large wheel, 87r=circumference of the largewheel. (17) The arc KZM=*-42 : ::8«-: (9 05 ft.) (18) 8tt—9 05= ft = KDM, part of circumference coveredby the belt. (19) Area of the sector MLKO=42 : l2:: : ( ) (20) 27r=circumference of small wheel. (21) The arc MLK= : : ( ft.) (22) ft., circumference of small wheel—, arc MK= ft., part of small wheel covered by belt. (23) ft+ ft.+ ft= ft., required length. {Eaton.)If the belt is not crossed, what is its length? Solution, (1) Let F, L, S and K be thepoints wherethe belttouches thewheels. (2) LZO andLFD are sim-ilar triangles. (3) LD : LO::FD : ZO; hence 3 : 4:: 12 : (16=OZ.) (4) Z0=Z0-00=4ft ZF=VZ7Q2—FO2= FIG. 65. (5) FL=VFD2—LU2 = V122— 3* = ft. (6) ft. X 2= ft, length of belt not touching thewheels. (7) Area of the triangle OLZ=(ZLx LO)|= sq. ft. (8) LP= ( 2) +16= ft., LK= ft. (9) PO = VLOa— CF* =1,008 ft. (10) PZ = ZO—PO= ft. (11) Area of the segment LZK=(ZP3-^by twice LK) + 184 FAIR CHILDS SOLUTION BOOK. f(ZPxLK)= ft. (12) Area of the triangle LKO=-J( LKx PO)= sq. ft. (13) Hence, the area of the sector OLKZ= sq. ft.+ sq. ft. (14) 4*7r : :: 8:r : ( ft.)=arc LZK, or part that thebelt does not touch of the large wheel. (15) 8tt— ft., part of large wheel covered bythe belt. (16) 42 : 12 :: : sq. ft., area of sector FMS, orpart of small wheel covered by belt. (17) .5*-V : Itt :: 1 273 : .509 ft., length of belt on small wheel. (18) .509 23 236 ft.+ ft = ft., required
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Keywords: ., bookcentury1800, bookdecade1890, booksubject, booksubjectgeometry
