Plane and solid geometry . of the other base. 977. Def. If the plane of one of the bases of a zone is tan-gent to the sphere, the zone is called a zone of one base. Thus, arc NA or arc RS will generate a zone of one base. 978. Questions. Is the term zone used in exactly the same sensehere as it is in the geography ? Name the geographical zones of one base ;of two bases. Name the five circles whose circumferences form thebases of the six geographical zones. Which of these are great circles ? * 979. Cor. II. The area of a zone is equal to the productof its altitude and the cirouwiference of a gr
Plane and solid geometry . of the other base. 977. Def. If the plane of one of the bases of a zone is tan-gent to the sphere, the zone is called a zone of one base. Thus, arc NA or arc RS will generate a zone of one base. 978. Questions. Is the term zone used in exactly the same sensehere as it is in the geography ? Name the geographical zones of one base ;of two bases. Name the five circles whose circumferences form thebases of the six geographical zones. Which of these are great circles ? * 979. Cor. II. The area of a zone is equal to the productof its altitude and the cirouwiference of a great circle. Outline •of Proof Let S denote the area generated bybroken line A^B^C\ s by broken lineABC, and Z by arc ABC; let BE, thealtitude of the zone, be denoted by H. Then -S = D^. 2 ttT? ; S = BE • 2 7ra. .-. - = —• (See Args. 2-5,s a^ § 969.) Then by steps similar to §§969-971, z = ^.2 7ri?. * The student will observe that the projection used in this figure is different from thatused in the other 450 SOLID GEOMETRY 980. Cor. m. In equal splveres, or in the same sphere^tlve areas of two zones are to each otlver as their altitudes. 981. Question. In general, surfaces are to each other as the prod-ucts of two lines. Is § 980 an exception to this rule ? Explain. Ex. 1553. The area of a zone of one base is equal to the area of acircle whose radius is the chord of the arc generating the Use §§ 979 and 444, II. Ex. 1554. Show that the formula of § 971 is a special case of § 1555. Find the area of the surface of a zone if the distancebetween its bases is 8 inches and the radius of the sphere is 6 inches. Ex. 1556. The diameter of a sphere is 16 inches. Three parallelplanes divide this diameter into four equal parts. Eind the area of eachof the four zones thus formed. Ex. 1557. Prove that one half of the earths surface lies within 30°of the equator. Ex. 1558. Considering the earth as a sphere with radius i?, find the 7? 2 7?area of th
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
