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" The volumes of similar solids are to each other as the cubes of their like dimensions. "
Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ... - Page 38
by Nathan Scholfield - 1845
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A Commercial Arithmetic: Designed for Academies, High Schools, Counting ...

James Bates Thomson - Business mathematics - 1884 - 344 pages
...Dimensions of similar surfaces are to each other as the square roots of their areas. 8°. The Contents of similar solids are to each other as the cubes of their like dimensions. Conversely, 4°. The Like Dimensions of similar solids are as the cube roots of their contents....
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Ohio Educational Monthly, Volume 35

Education - 1886 - 712 pages
...2960 =7280 cu. in., the top of the pyramid after one-half the solidity of the post has been taken off. Similar solids are to each other as the cubes of their like dimensions; hence. 10240 : 7280 ; ; (480)* : x. Solving the proportion and extracting the cube root,...
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The New Model Arithmetic

Henry Holmes Belfield - Arithmetic - 1891 - 362 pages
...is 20. 4. How many square miles on the surface of the earth, assuming the diameter to be 8000 miles. Similar solids are to each other as the cubes of their like dimensions. Thus, spheres are to each other as the cubes of their diameters or radii 5. How many balls...
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Table Book and Test Problems in Mathematics

John Kelley Ellwood - Algebra - 1892 - 300 pages
...and the next one, taken together, formed a cone whose volume was f of the loaf. Hence, observing that similar solids are to each other as the cubes of their like dimensions, we have the following proportions: 3:1 ::203: A3, whence ft = 20v/|=;jy>-v'9 = 13.86722...
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Standard Arithmetic: Embracing a Complete Course for Schools and Academies

William James Milne - Arithmetic - 1892 - 440 pages
...SIMILAR VOLUMES. The truth of the following principles can be shown by geometry : 467. PRINCIPLES. — 1. Similar solids are to each other as the cubes of their like dimensions. Hence, 1. If a globe 4 inches in diameter weighs 8 lb., what will be the diameter of a...
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Dubbs' Complete Mental Arithmetic: A Volume of Carefully Graded Exercises ...

Eugene L. Dubbs - Arithmetic - 1893 - 238 pages
...the like dimensions of two similar figures is equal to the square root of the ratio of their areas. Similar solids are to each other as the cubes of their like dimensions ; therefore, The ratio of two similar solids is equal to the cube of the ratio of their...
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Graded Lessons in Number, Part 2

Wm. M. Peck - 1894 - 310 pages
...bushels will it hold? SIMILAR SOLIDS. Similar Solids are solids whose shapes are alike. I. The volumes of similar solids are to each other as the cubes of their like dimensions. Solve the following problems : 1. One sphere is 3 feet in diameter ; another sphere is...
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Concrete Geometry by the Inductive Method ...

J. R. Bevis - Geometry - 1896 - 174 pages
...planes are to each other as the squares of their like dimensions, can you prove that the solidities of similar solids are to each other as the cubes of their like dimensions ? 2. The weight of a cubic foot of water is 62 pounds: what is the weight of a similar body...
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The Rand-McNally Practical Arithmetic: Complete for All Ordinary Purposes

Edwin Crawford Hewett - Arithmetic - 1897 - 376 pages
...is 18 in. 287. Similar Solids. 1. Similar solids are such as have the same shape. 2. The volumes of similar solids are to each other as the cubes of their like dimensions. EXERCISES. 288. 1. The sides of two cubes are to each other as 3 to 5. If the smaller one...
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Lippincott's Practical Arithmetic: Embracing the Science and Practical ...

James Morgan Rawlins - Arithmetic - 1899 - 458 pages
...of a similar piece of land having twice the length and breadth ? Similar Solids. 1. The volumes of similar solids are to each other as the cubes of their like dimensions. PROBLEMS. 1. Of two spheres, one is 1000 times the size of the other. If the diameter of...
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