This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1919 edition. Excerpt: ...the opposite side. Find the volume and area of the figure developed by revolving the triangle about the line l. Suggestion. The volume may be obtained by subtracting the volumes of two cones from the volume of a cylinder. 12. Through a vertex of a square with sides a draw a line l perpendicular to the ... Read More
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1919 edition. Excerpt: ...the opposite side. Find the volume and area of the figure developed by revolving the triangle about the line l. Suggestion. The volume may be obtained by subtracting the volumes of two cones from the volume of a cylinder. 12. Through a vertex of a square with sides a draw a line l perpendicular to the diagonal at that point. Find the area and volume of the figure developed by turning the square around l. Suggestion. Notice that two frustums and two cones are developed. 13. In a regular hexagon with sides a draw a line l bisecting two opposite sides. Find the area and volume of the figure developed by turning the hexagon about l as an axis. 14. One angle of a right triangle is 30. Find the ratios of the surfaces and also of the volumes of the solids developed by revolving this triangle around each of its three sides in succession. G_ jf Suggestion. The sides of the A are a, 2 a aVS. 15. If through any point P in a diagonal of a parallelopiped planes KN and BM are drawn parallel to two faces, show that the parallelopipeds DQ and LN thus formed have equal volumes. Archimedes (287-212 B.c. ) was without doubt the greatest mathematician of his time. He is known not through any extended treatise, like that of Euclid, but through a series of monographs on practically every mathematical subject then known, including physics, mechanics, astronomy, and many phases of geometry. His work on the circle, cone, cylinder, and sphere is reflected in our treatment of surfaces and volumes at the present day. BOOK V THE SPHERE 276. Sphere, Center. A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the center. 277. Diameter. Radius. A line-segment connecting two points on the surface of a sphere and... Read Less
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