# An Elementary Treatise on Mensuration

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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. 1881 edition. Excerpt: ... 3: 250,047, g(S). IRREGULAR SOLIDS. 96. Any small solid may be estimated by placing it in a vessel of convenient shape, such as a quader or a cylinder, and pouring in a liquid until the solid is quite covered; then noting the level, removing the solid, and again noting the level at which the liquid stands. The volume of the solid is equal to the volume of the vessel between the two levels. 97. If the solid is homogeneous, weigh it. Also weigh a cubic centimeter of the same substance. Divide the weight of the solid by the weight of the cubic centimeter. The quotient will be the number of cubic centimeters in the solid. From 73, we have the Formula: Yccm =. 8 Exam. 92. A ball 5 centimeters in diameter weighs 431-97 grams. An irregular solid of the same substance weighs 132 grams; find its volume. The volume of the ball is 53 x 0-5236 = 65-45..-. 431-97--65-45 = 6-6 grams, the weight of a cubic centimeter..'. 13-2 6-6--2 cubic centimeters. Arts. 98. To find the volume of any irregular polyhedron. Eule: Cut the polyhedron into prismatoids by passing parallel planes through all its summits. Formula for n consecutive prismatoids: 1= i x2(B, -BB) + x3(B2-BA) + eta. + i x2M1 + (8-x2)M2 + fa-xs)Mz + etc. + xn+1-xn)Mn. Note. X2 is the distance of B2 from Bt) and x3 is the distance of Bz from Bv etc. Proof: This formula is obtained directly by the method of 41. CHAPTER VI. The Applicability Of The Prismoidal Formula. 99. To find whether the volume of any solid is determined by the Prismoidal Formula. Eule: The Prismoidal Formula applies exactly to All Solids contained between two parallel planes, Of Which the area of any section parallel to these planes can be expressed by a rational integral algebraic junction, of a degree not higher than the third, of its...