QUEST.-7. If a cone be cut by a plane parallel to the base, what will the section be? If the upper part be taken away what is the lower part called? 8. What is the convex surface of a cone equal to? 9. What is the solidity of a cone equal to ? Of the Round Bodies. 10. Since the solidity of a cylinder is equal to the base multiplied by the altitude (Art. 5), and that of a cone to the base multiplied by one third of the altitude, it follows that if a cylinder and cone have equal bases and altitudes, the cone will be one-third of the cylinder. 11. A Sphere is a solid terminated by a curved surface all the points of which are equally distant from a certain point called the centre. 12. The sphere may be described by revolving a semicircle ABD about the diameter AD. The plane will describe the solid sphere, and the semi-circumference ABD will describe the surface. B QUEST.-10. If a cylinder and cone have the same base and altitude, which will be the greater? How much will the cylinder exceed the cone ? 11. What is a sphere? 12. How may a sphere be described? What will the plane describe? What will the semicircumference describe? 13. What is the radius of a sphere? 15. All diameters of a sphere are equal to each other; and each is double a radius. 16. The axis of a sphere is any line about which it volves; and the points at which the axis meets the surface, are called the poles. and go and quad Him abub, howled I bumi butex wit 17. A Plane is tangent to a sphere when it has but one point in common with it. Thus, AB is a tangent plane. QUEST.-14. What is the diameter of a sphere? 15. Are all diameters equal? How does a diameter compare with a radius? 16. What is the axis of a sphere? What are the poles of a sphere? 17. When is a plane said to be tangent to a sphere? Of the Round Bodies. 18. A zone is a portion of the surface of a sphere, included be tween two parallel planes which D are two circles whose diameters are AE and DF 19. One of the planes which bound a zone may become tangent to the sphere, in which case the zone will have but one base. Thus, if one plane be tangent to the sphere at A, and another plane cut it in the circle DF, F the zone included between them will have but one base. 20. A spherical segment is a portion of the solid sphere included hetween two parallel planes. These parallel planes are its bases. If one of the planes is tangent to the sphere, the segment will have but one base. QUEST.-18. What is a zone? What are the bases of a zone? 19. If one of the planes which bound the zone becomes tangent to the sphere, how many bases will the zone have? 20. What is a spherical segment? What are the parallel planes called? If one of the parallel planes becomes tangent to the sphere, how many bases will the segnent have? Of the Round Bodies. 21. The altitude of a zone or segment, is the distance between the parallel planes which form its bases. 22. Every plane passing through a sphere intersects the solid sphere in a circle, and the surface of a sphere in the circumference of a circle. 23. If the intersecting plane passes through the centre of the sphere, the circle is called a great circle. If it does not pass through the centre, the circle of section is called a small circle. 24. The surface of a sphere is equal to the product of its diameter by the circumference of a great circle. Thus, the surface E of the sphere whose centre is C, is equal to circumference ABDEX AD. B QUEST.-21. What is the altitude of a zone or segment? 22. If a plane be passed through a sphere, in what will it intersect the solid sphere? In what will it intersect the surface? 23. If the intersecting plane passes through the centre of the sphere, what is the circle called? If it does not pass through the centre of the sphere, what is the circle called? 24. What is the surface of a sphere equal to ? |