232 FARM ARITHMETIC. 



6^ feet long and 6 inches square at the bottom and SjA 

 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 

 V/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>4 inches 

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

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



X X + 78 

 Therefore, = ^- 



3^ 6 



6X = 3i^X + 3^ X 78 



6X — 3i^X = 3^ X 78 



214X = 3H X 78 

 " 5X = 7 X 78 = 546 

 " X = 109.2 Inches, altitude smaller pyramid. 



X + 78 = 187.2 Inches, altitude larger pyra- 

 mid. 



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 H- 1,728 = 1.04 Cubic feet. 



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



approximately 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 7>4 feet high, omitting roof 



