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Elementary Pure Geometry with Mensuration; A Complete Course of Geometry for Schools

Elementary Pure Geometry with Mensuration; A Complete Course of Geometry for 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. 1904 Excerpt: ...the sphere in a great circle--e.g. line of longitude. Great circles can be moved about on a sphere just as straight lines on a plane; and one only can be drawn between two points, unless these are opposite ends of a diameter of the sphere. 'The area of a sphere is four times the area of a great circle;' i.e. area = 4irr2. Volume Op A Sphere. If the sphere is divided into small pyramids by planes through the centre, the volume of a pyramid is area of base x altitude (radius). And the volume of the sphere--i.e. the sum of the pyramids--is that of a pyramid whose base is the surface of the sphere, and altitude the radius; thus--'The volume of a sphere is one-third the product of radius and surface;' i.e. vol. of sphere =----o Ex. 1. Calculate the surface and volume of spheres of radii 2 cm., 1-6," 5 ft. Ex. 2. Taking a degree as 69-12 miles, calculate the earth's circumference (length of a great circle). Ex. 3. Taking the earth's radius as 3960 miles, calculate its circumference, and its area. The proof is given below, Ch. IX. EXAMPLES--XXVIII. 1. Calculate the volume of a room 24 ft. long by 18 ft. wide and 12 ft. high. 2. Calculate the area of a box 33" by 16" by 18." 3. Calculate the volume of a pile of books 100 deep, each book 84" by 6" by 4. How much water is required to fill a stretch of canal 3 miles long, 6 ft. deep, 24 ft. wide? Answer in cubic yards. 5. A wedge has a triangular base of sides 3," 4," 5," and an altitude of 6." Calculate its volume. 6. A cuboid block of wood 2 ft. by 1 ft. by 3" is sawn across the diagonals of its greatest faces so as to form four wedges. Calculate the volume of each. 7. How many cubic inches of milk does a can 1 ft. high, 1 ft. diameter, hold? 8. If 1 gallon cont...


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Product Details
  • ISBN-13: 9781152646292
  • Publisher: General Books
  • Publisher Imprint: General Books
  • Height: 229 mm
  • No of Pages: 174
  • Spine Width: 10 mm
  • Width: 152 mm
  • ISBN-10: 115264629X
  • Publisher Date: 03 Jan 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 263 gr

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Elementary Pure Geometry with Mensuration; A Complete Course of Geometry for Schools
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