The principles of plane trigonometry, mensuration, navigation and surveying - Softcover
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. 1831 Excerpt: ...Therefore the area of all the equal trapezoids which form the lateral surface of Sea note F. the frustum, is equal to the product of half the slant-height into the sum of the perimeters of the ends. Ex. If the slant-height of a frustum of a regular octagonal pyramid be 42 feet, the sides of one end 5 feet each, and the sides of the other end 3 feet each; what is the lateral surface?, Ans. 1344 square feet. 52. If the slant-height be not given, it may be obtained from the perpendicular height, and the dimensions of the two ends. Let GD (Fig. 17.) be the slant-height of the frustum CDGL, RN or GP the perpendicular height, ND and RG the radii of the circles inscribed in the perimeters of the two ends. Then PD is the difference of the two radii: And the slant-height GD = x/(GP3+YD3). Ex. If the perpendicular height of a frustum of a regular hexagonal pyramid be 24, the sides of one end 13 each, and the sides of the other end 8 each; what is the whole surface? t/(BC-BP)=CP,(Fig.7.)thati8,.v/(l33-633)=11.258 And V'83--43 e= 6.928 The difference of the two radii is, therefore, 4.33 The slant-height =V(243 + 4.333)=24.3875 The lateral surface te 1536.4 And the whole surface, 2141.75. 53. The height of the whole pyramid may be calculated from the dimensions of the frustum. Let VN (Fig. 17.) be the height of the pyramid, RN or GP the height of the frustum, ND and RG the radii of the circles inscribed in the perimeters of the ends of the frustum. Then, in the similar triangles GPD and VND, DP: GP::DN: VN. The height of the frustum subtracted from VN, gives VR the height of the small pyramid VLG. The solidity and lateral surface of the frustum may then be found, by subtracting from the whole pyramid, the part which is above the cut ting plane. This method may serve to ...
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- PublisherRarebooksclub.com
- Publication date2012
- ISBN 10 1130655547
- ISBN 13 9781130655544
- BindingPaperback
- Number of pages96
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