School: a monthly record of educational thought and progress . Fig. 6.—Cone and Cylinder equal to Sphere. Volume of this cylinder = end x height = TT r^ y. r = IT ??. „ ,, cone = J end x height = \-Kr- y. r = \irr^. and volume of sphere = the cylinder + cone, = TT r^ + Inr^3 = I J- 7r >^ or 4 TT y^. When the difference between the formulae for thesurface of the sphere, and for the volume of a spherehave been practically demonstrated by the meansindicated in this article, the confusion between the two,which is so often seen in examination papers, is renderedalmost impossible. Definitions of
School: a monthly record of educational thought and progress . Fig. 6.—Cone and Cylinder equal to Sphere. Volume of this cylinder = end x height = TT r^ y. r = IT ??. „ ,, cone = J end x height = \-Kr- y. r = \irr^. and volume of sphere = the cylinder + cone, = TT r^ + Inr^3 = I J- 7r >^ or 4 TT y^. When the difference between the formulae for thesurface of the sphere, and for the volume of a spherehave been practically demonstrated by the meansindicated in this article, the confusion between the two,which is so often seen in examination papers, is renderedalmost impossible. Definitions of Cone, Cylinder, and Sphere. The apparatus in Fig. 7 visualises the generation ofthe cone, cylinder and sphere, with the result that EDUCATIONAL THOUGHT AND PROGRESS 41 students are at once able to give correct mathematicaldefinitions of these solids. The rotating part is painted. Fig. 7.—Models in stiff wire or thin strips of metal, which onrotating trace out Cone. Cylinder and Sphere. white, and the rest of the apparatus a dull black, makingthe ghost of a cone, cylinder, or sphere—as the casemay be—visible to a large class. The way has nowbeen paved for the introduction of Oblique Solids,as distinguished from Right Solids. (iv) Oblique Prisms and Pyramids.—Fig. 8 illus-trates samples of these oblique models. These are in
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