232 FARM ARITHMETIC. 



6 */2 feet long and 6 inches square at the bottom and 8^2 

 inches square at the top? 



Process : A solid of this shape is called a frustum of a pyra- 

 mid. It may be regarded as the solid that is left when a pyra- 

 mid having a base 6" x 6" has a pyramid having a base 3}4" x 

 zy 2 " removed from its top. If the height of the smaller pyramid 

 in inches be represented by X, then we must have the relation: 

 X inches (the altitude of the smaller pyramid) is to 3^ inches 

 (the side of its base) as X -f 78 inches (the altitude of the 

 larger pyramid) is to 6 inches (the side of its base). 



X X + 78 



Therefore, = 



3^ 6 



6X = 3^X + 3y 2 X 78 

 6X 3^X = 3*/ 2 X 78 

 2^X = y/ 2 X 78 

 5X = 7 X 78 = 546 



X = 109.2 inches, altitude smaller pyramid. 

 X -|- 78= 187.2 inches, altitude larger pyramid. 



The volume of a pyramid is equal one-third the area 

 of the base multiplied by the altitude. 



The volume of the larger pyramid is 



1/3 X 6 X 6 X 187.2 = 2,246.4 cubic inches. 

 The volume of the smaller pyramid is 



1/3 X 3.5 X 3.5 X 109.2 = 445.9 cubic inches. 

 Volume of post = 2,246.4 445.9 = 1,800.5 cubic inches. 

 . ' . volume of post = 1,800.5 -f- 1,728 = 1.04 cubic feet 

 Volume of 50 posts = 50 X 1-04 = 52 cubic feet, or approx- 

 imately 2 cubic yards. 



857. If the above posts were the same size at the top 

 as at the bottom, how many cubic yards would be re- 

 quired? If 10" x 10" at bottom and 6" x 6" at top i. e., 

 corner-post size? 



858. How much No. 6 wire is required to reinforce 

 the 50 posts in the above problem if each post contains 

 four strands running the entire length ? 



859. How much concrete is required to build a root 

 cellar 10 feet by 14 feet and iy 2 feet high, omitting roof 



