MEASURES OF VOLUME. 215. Anything which has length, breadth, and thickness is called a Solid. 216. A solid having six equal square sides or faces is called a Cube. A cube whose sides or faces are each a square inch is called a Cubic Inch. One whose sides are each a square foot is called a Cubic Foot. One whose sides are each a square yard is called a Cubic Yard. 1 Inch. 217. The number of solid units any body contains is its Solid Contents or Volume. Thus, if a solid is 4 ft. long, 3 ft. wide, and 3 ft. thick, its solid contents or volume is 36 cubic feet. For it may be divided into 3 blocks, each containing 12 cubic feet. The number of cubic feet in each block is equal to the product of the numbers expressing the length and breadth of the solid, and the number of blocks is equal to the number of units of thickness. Therefore, 218. PRINCIPLE. The volume of any rectangular solid is equal to the product of the numbers expressing its length, breadth, and thickness. The length, breadth, and thickness must be expressed in units of the same denomination. 1. How many cubic inches are there in a rectangular solid 3 in. long, 2 in. wide, and 2 in. thick? 2. How many cubic inches are there in a rectangular solid 1 ft. long, 1 ft. wide, and 1 ft. thick, or a cube whose edge is 1 ft.? 15. Reduce of a cu. yd. to units of lower denominations. 16. Reduce of a cu. ft. to cubic inches. 17. Reduce of a cu. yd. to cubic feet and inches. 18. Reduce .675 of a cu. ft. to cubic inches. 19. Reduce of a cu. ft. to a fraction of a cubic yard. 20. Reduce 8 cu. ft. 240 cu. in. to the decimal of a cubic yard. 21. A man bought a block of marble 4 ft. 9 in. long, 2 ft. 7 in. wide, and 2 ft. 5 in. thick. How much did he pay for it at the rate of $15.80 per cubic yard? SURVEYORS' MEASURES. SURVEYORS' LINEAR MEASURE. 219. Surveyors, in measuring, use a chain consisting of 100 links, its length being 4 rods, or 66 feet. 1. Since a chain contains a hundred links, how many links make a rod ? 2. How many rods make a mile? How many chains? 3. How many inches are there in a chain, or 66 ft. ? 4. Since there are 100 links in a chain, what is the length of each link? 5. Write a table of surveyors' linear measures. 6. How many links in 2 rd. ? Reduce to links: 1. 40 rd. 15 1. In 3 rd.? In 4 rd.? In 32 rd.? In 40 rd.? WRITTEN EXERCISES. 2. 3 rd. 12 1. 3. 5 rd. 15 1. 4. 7 ch. 2 rd. 14 1. 5. 25 ch. 3 rd. 20 1. 6. 40 ch. 60 1. 7. 75 ch. 75 1. 8. 12 mi. 16 ch. 20 1. 21. Reduce of a chain to the fraction of a mile. 22. Reduce of a chain to links. 23. Reduce 28 links to a fraction of a chain. SURVEYORS' SQUARE MEASURE. 220. 1. How many links are there in a rod? How many square links are there in a square rod? 2. How many rods are there in a chain? How many square rods are there in a square chain? 3. How many rods are there in an acre? square chains are there in an acre? How many 4. Write a table of surveyors' square measures. WRITTEN EXERCISES. Reduce to units of lower denominations: 1. 5 sq. ch. 2. 2 acres 8 sq. ch. 3. g of a chain. 4. 240 acres 15 sq. ch. 5. 3 sq. mi. 18 A. 15 sq. ch. 6. .645 of an acre. Reduce to units of higher denominations : 221. 1. How many gills are there in 7 WRITTEN EXERCISES. Reduce to units of lower denominations: pt.? In 10 pt.? In 8 qt.? In 10 qt. ? In 68 pt. ? 20. Reduce 1 pt. 2 gi. to the decimal of a gallon. DRY MEASURE. 222. 1. How many pints are there in 10 qt.? 2. How many quarts are there in 8 pk.? In 12 qt.? In 10 pk.? 3. How many quarts are there in a bushel? How many pints? In 3 bushels how many quarts? How many pints? 4. How many pecks are there in 33 qt.? 5. How many pecks are there in 18 pt.? 6. How many bushels are there in 20 pk.? Reduce to pints : WRITTEN EXERCISES. In 41 qt.? In 24 pt.? In 25 pk.? 18. Reduce 19. Reduce of a pint to the fraction of a bushel. of a quart to the fraction of a bushel. 20. Reduce 3 pk. 7 qt. to the decimal of a bushel. |