A complete and practical solution book for the common school teacher . FIG. 63. (3) DOF= J of a circle, or a quad- rant, but the horse grazes over£ of a circle, or FED. (4) As f of a circle = 20 A., then there must be 6J A. in thequadrant DOF. (5) 26J of the circle. (6) R27r=area of the circle. (7) /. R27r=26f A., or 4266f sq. rd.* (8) R= rd., the length of the rope. PROBLEM 378. A wheel 8 ft. in diameter is run by means of a belt from a wheel 1ft. in radius; the distance between their centers is 12 ft., and the beltis crossed between them, causing- them to revolve in opposite dir
A complete and practical solution book for the common school teacher . FIG. 63. (3) DOF= J of a circle, or a quad- rant, but the horse grazes over£ of a circle, or FED. (4) As f of a circle = 20 A., then there must be 6J A. in thequadrant DOF. (5) 26J of the circle. (6) R27r=area of the circle. (7) /. R27r=26f A., or 4266f sq. rd.* (8) R= rd., the length of the rope. PROBLEM 378. A wheel 8 ft. in diameter is run by means of a belt from a wheel 1ft. in radius; the distance between their centers is 12 ft., and the beltis crossed between them, causing- them to revolve in opposite direc-tions: what is the length of the belt used? Solution. (1) OMandOMare parallel;O M P a n dO M P aresimilar tri-angles. (2) Hence, wehave the pro-portion, OM : OM :: OP: OP. (3) Now, PO=*, OP=12-*. (4) 4:1::^: 12—.*, whence *= ft. (5) OP = 12 ft.— ft. ft. KP:. FIG. 64. (6) PK=:VPO2—KC (7) KP = Vop2_oK2r= ft. (8) KK=KP+PK= (9) Hence, MM+KK= ft. = length of the belt not onthe wheels. MENSURA TION. 183 (10) KfS=(PKxKOf)-f-PO= (11) KM= 2= 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 len
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