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Mensuration for Elementary and Middle Class Schools

Mensuration for Elementary and Middle Class Schools


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: ...14. The surface of a globe contains 6 sq. yds. 2 7449 ft.; find its diameter. 15. A spherical body contains 2 80957 cub. ft.; what is its circumference? 16. The diameter of the sun is 112 times greater than that of the earth; how many times greater is its volume? Lesson XX.--Frustrum Of Pyramid Or Cone. A frustrum is a solid figure formed by cutting off the top of a pyramid or cone by a plane parallel to the base. In most instances the solidity of a frustrum may be conveniently found by first finding that of the whole pyramid or cone of which it is a part, and then subtracting the solidity of the piece which is cut off. But in cases where this not convenient, the calculation may be made as follows: --Let us begin with the frustrum of a triangular pyramid, DCBFE. Now, if a plane be made to pass through ABD, and another through ABE, the frustrum will be divided into three pyramids, viz., ABCD, whose base is the base of the frustrum, and height the height of the frustrum; ABFE, whose base is the top of the frustrum AFE, and height the height of the frustrum; and AEDB, whose base is the triangle BDE, and whose vertex is at A. But this last pyramid can be proved to be equal to a pyramid whose height is that of the frustrum, and base a mean proportional between the top and base of the frustrum. Now these three pyramids taken together make up the whole frustrum, and if A represent the area of the base, a, that of the top, and h the height, then h (1.) Volume of 1st pyramid =-A. (2.) 2nd h (3.) 3rd g-V Ao. h.." Volume of frustrum = Tt (A + a + /Aa). Now it is evident that a frustrum with a polygonal base may be treated in the same way, and that since the circle is merely a regular polygon with innumerable sides, the frustrum of a...


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Product Details
  • ISBN-13: 9781130003253
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 28
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130003256
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 68 gr

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