 | Rufus Putnam (Arithmetician) - 1849 - 164 σελίδες
...cube root of the solidity of the latter. The whole truth may be thus expressed. • The contents of similar solids are to each other as the cubes of their like dimensions ; and like dimensions of similar solids are to each other as the cube roots of their contents. Hence,... | |
 | George Roberts Perkins - 1850 - 356 σελίδες
...root of , 1 5 to 8 decimals ? Ans. 0-13992727. EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 79. IT is an established theorem of geometry, that all...other as the cubes of their like dimensions. 1. If a cannon ball 3 inches in diameter weigh 8 pounds, what will a ball of the same metal weigh, whose diameter... | |
 | George Roberts Perkins - 1851 - 356 σελίδες
...the cube root of f ? Ans. 0-8736, nearly. EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE RCflT 136. It is an established theorem of geometry, that all similar solids are to each other as the cubes of their likt dimensions. 1. If a cannon-ball, 3 inches in diameter, weigh 8 pounds, what will a ball... | |
 | Thomas Tate - 1853 - 396 σελίδες
...~ • — -. frustum ABED o Put co = a, cR=au and »»=cone ABC; then CG=- a, CGj o = - a, ; and as similar solids are to each other as the cubes of their like dimensions, cone DEC=-^ m, frustum ABED=»» — '3 m f (t^\ =ml 1 's J ; therefore by substitution 3 3 a,3 . _4ax«,—-alX-8-,«... | |
 | Dana Pond Colburn - 1855 - 396 σελίδες
...solidities of spheres are to each other as the cubes of their radii or diameters. (<,.) The solidities of similar solids are to each other as the cubes of their like dimensions. (p.) The solidity of a prism equals the area of its base multiplied by its altitude. (q.) The solidity... | |
 | George Roberts Perkins - 1856 - 460 σελίδες
...as given in the table, and the sum will be the logarithm of the surface. Again, since the volumes of similar solids are to each other as the cubes of their like dimensions, we may find the volume of any regular polyedron by this KULE. Multiply the cube of one of the edges... | |
 | Dana Pond Colburn - 1856 - 392 σελίδες
...other as the cubes of their radii or diameters. • See foot note, page 34.3. (o.) The solidities of similar solids are to each other as the cubes of their like dimensions. (p.) The solidity of a prism equals the area of its base multiplied by its altitude. (q.) The solidity... | |
 | Dana Pond Colburn - 1858 - 288 σελίδες
...of 3 ft. radius contains 27 as many cubic feet as a sphere of 2 ft. radius. (n.) The solidities of similar solids are to each other as the cubes of their like dimensions. ILLUSTRATION. — A cube 2 ft. on a side is to a cube 5 ft. on a side as 2' is to 5", or as 8 is to... | |
 | Charles Haynes Haswell - 1858 - 350 σελίδες
...166)=39.27, ^ of which=7.854. Put x=su=the immersed part of the axis of the sphere, and C «=C s Then, as similar solids are to each other as the cubes of their like dimensions, 6' : (3.2+x)':: 39.27: cone nCr; .-.cone n C r=(8.2'f ^'x 39.2 7. 216 Segment rfs/(by rule 2, p. 177)=(4x3-2r)xx3x.5236... | |
 | Silas Lawrence Loomis - 1859 - 324 σελίδες
...above result. By the short method, 125. 8464 3 253112 2208 64 2208 SECTION IV. MENSURATION OF SOLIDS. All similar solids are to each other as the cubes of their like dimensions. PROB. CXXX. — To FIND A SIDE OF A CUBE. RULE. — Er/rac/ the cube root of its contents. PROB. CXXXI.... | |
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The volumes of similar solids are to each other as the cubes of their like dimensions. 
