 | George Roberts Perkins - Arithmetic - 1850 - 364 pages
...INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 136. It is an established theorem of geometry, that all similar solids are to each 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... | |
 | George Roberts Perkins - Arithmetic - 1850 - 356 pages
...EXAMPLES INVOLVING THE PRINCIPLES OF THE CUBE ROOT. 79. IT is an established theorem of geometry, that all similar solids are to each 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... | |
 | Thomas Tate - Mechanical engineering - 1853 - 396 pages
...~ • — -. 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... | |
 | Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...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.)... | |
 | George Roberts Perkins - Arithmetic - 1855 - 388 pages
...EXAMPLES INVOLVING THE PRINCIPLES OF THE COBE RCOX 13G. It is an established theorem of geometry, that all similar solids are to each 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... | |
 | Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...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.)... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...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... | |
 | Dana Pond Colburn - 1858 - 288 pages
...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... | |
 | Charles Haynes Haswell - Measurement - 1858 - 350 pages
...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... | |
 | Anthony Nesbit - Measurement - 1859 - 494 pages
...are inscribed ; or as the squares of the diameters of those circles. {Em. TV. 36.) THEOREM XX. All similar solids are to each other, as the cubes of their like dimensions. (Em. VI. 24.) AN EXPLANATION PRINCIPAL MATHEMATICAL CHARACTERS. THE sign or character =... | |
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The volumes of similar solids are to each other as the cubes of their like dimensions. 
