CUBE 



1662 



CUBE ROOT 



CUBE, a regular solid having six equal 

 square faces. By solid is meant a body having 

 three dimensions length, breadth and thick- 

 ness. In finding the volume or contents of a 

 solid, that is, the space it occupies, the cube is 

 used as a unit of 

 measure, and the 

 result is expressed 

 in cubic inches, 

 cubic feet, etc. 

 The volume of a 

 cube is found by 

 using three times 

 as a factor the 

 number which 

 expresses the 

 length of one of 



,-J r, . 4-V.of it ne ngure, reduced in size, 



1S represents a cubic foot. Each 



a cube whose fac e is twelve inches in 



. . . length and width. The vol- 



edge is 4 inches ume is 12x12x12 inches, or 



in Ipnirth rnntflins 1.728 cubic inches. The small 



mtains black cube is one -twelfth of 



4X4X4, or 64, the length, breadth and thick- 



.... _, ness, or one cubic inch. There 



cubic inches, .tor are 1,728 such small cubes 



this reason the in the entlre body - 

 third power of any number, which is the prod- 

 uct of that number taken three times as a 

 factor, is called its cube; for example, the cube 

 of 2 is 8; the cube of 3 is 27. For practical 

 application of the theory of the cube and its 

 relations, see CUBIC MEASURE; MENSURATION. 



CUBEBS, ku'bebs, the dried, unripened 

 berries of a shrub belonging to the pepper 



A CUBE 

 The figure, reduced in size, 



PARTS OF CUBES PLANT 

 (a) Branch; (6) flower; (c) berry growing 

 from flower stalk. 



family, the piper cubeba. It is used in Eastern 

 countries as a -flavoring and in Europe and 

 America for medicinal purposes. The shrub is 



native to Pcnang, Sumatra, New Guinea and 

 neighboring islands. The dried berries look 

 much like black pepper, but are less pungent 

 and of more agreeable flavor than that spice. 

 The drug prepared from cubebs acts as a stim- 

 ulant and is sometimes used in treating indiges- 

 tion. When prepared in the form of cigarettes 

 cubebs are sometimes thought to afford relief 

 for hay fever, asthma and inflammation of the 

 pharynx. 



CUBE ROOT. When it is desired to find the 

 length of one of the sides of a cube, that 

 fact is usually ascertained by actual measure- 

 ment. If, however, the number of cubic units 

 in the volume of the cube is known, the length 

 of any side may be found by figuring the cube 

 root of the number representing the volume. 

 The cube root of a number is one of its three 

 equal factors, as illustrated below. The knowl- 

 edge of how to find the cube root of large 

 numbers is not of great practical importance 

 to the average person, but such problems have 

 considerable value for mental discipline, and 

 they are interesting exercises to anyone with 

 a taste for mathematics. We will begin this 

 subject with a study of the roots of small 

 numbers : 



2X2X2 = 8; 8 is the cube of 2, and 2 is the 

 cube root of 8. 



12X12X12 = 1728; 1728 is the cube of 12. 

 and 12 is the cube root of 1728. 



The cube of 6 is written 6 3 . The small figure 3 

 is called the exponent. 



The cube root of 216 is written v'TTB". The 

 V/ is called the root sign, or radical sign. 



How to read the indicated operations : 



I. 6 may be read in full, as follows : 



(a) Multiply 6 by 6, and that product by 6 ; 



(b) Use 6 as a factor 3 times; 



(c) The third power of 6 ; 



(d) The cube of 6 ; 



(e) 6 cubed. 



II. ty 64 is read as follows : 



(a) What number used as a factor 3 times 

 gives 64? It can be seen clearly this way: nXn 

 Xn = 64. What is n? 



(b) Cube root of 64. 



It may be written n 3 = 64 and read, "What 

 number cubed gives 64?" This use of n should 

 be common in the arithmetic class ; it is very 

 helpful in making things clear, but should be read 

 "number" or "what number," not read "n." 



Exercise in reading: 



(1) 4 a =4X4X4 = 64. 



( 4 used as a factor three times is 4X4X4 = 

 64.) 



(2) 6=6X6X6 = 216. 



(6 cubed is 6x6x6 = 216.) 



(3) 



(Read just as they appear.) 



