An introduction to mensuration and practical geometry Book PDF, ePub eBook

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Book Descriptions:
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. 1829 Excerpt: ...1.25, 1.25 and 1.25=3 differences. Whence /3.75X 1.25X1.25X 1.25=/3.75 X l7253 = /7.32421875=2.7063=arca of the base as before, And 2.7063X10=27.063 solid feet, the content of the prism required, 2. What is the solidity of a triangular prism, whose length is 18 feet, and one side of the equilateral end 1$ feet? Ans. 17.5370265 feet. 3. Required the solidity of a prism whose base is a hexagon, supposing each of the equal sides to be 1 foot 4 inches, and the length of the prism 15 feet. Ans. 69.282ft. PROBLEM IV. To find the convex surface of a cylinder. RULE.t Multiply the periphery or circumference of the base, by the height of the cylinder, and the product will be the convex surface required.. EXAMPLES. 1. What is the convex surface of the right cylinder ABCD, whose length BC is 20 feet, and the diameter of its base AB 2 feet 1 See Notes to Prob. III. Cor. ft. p. 56. t Demon. If the periphery of the base be conceived to move ia a direction parallel to itself, it will generate the convex superficies of the cylinder, and, therefore, the said periphery being multiplied by the length of the cylinder, will be equal to that superficies. Q. E. D. Note. If twice the area of either of the ends be added to the convex surface, it will give the whole surface of the cylinder. Here 3.1416 X 2=6.2832=periphery of the base AB. And 6.2832X20=125.6640 square feet, the convexity required. 2. What is the convex surface of a right cylinder, the diameter of whose base is 30 inches, and the length 60 inches 1 Ans. 5654.88 inches. 3. Required the convex superficies of a right cylinder, whose circumference is 8 feet 4 inches, and its length 14 feet, Ans. 116.666, dfc.feet. PROBLEM V. To find the solidity of a cylinder. RULE. Multiply the area of the base by the perpendicular heigh...

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