213. The number of square units in the surface of anything is called its Area. Thus, if a rectangle is 4 inches long and 3 inches wide, the area will be 12 square inches. For it may be divided into 4 rows, each containing 3 square inches or units, and the entire area will be 12 square inches. tangle is equal to the product of the numbers that express its length and breadth. The length and breadth must be expressed in units of the same denomination; the product will then express the area in square units of the same name. 1. How many square inches are there in the surface of a rectangle that is 6 in. long and 4 in. wide? In one 8 in. long and 5 in. wide? In one 7 in. long and 6 in. wide? 2. How many square feet are there in the surface of a rectangle 9 ft. by 5 ft.? In one 8 ft. by 7 ft.? In one 10 ft. by 8 ft.? 3. How many square inches are there in a square whose sides are 5 in.? 6 in.? 8 in.? 12 in., or 1 ft.? How many square inches, then, are there in a square foot? 4. How many square feet are there in a square whose sides are 2 ft.? 3 ft., or 1 yd.? How many square feet are there, then, in a square yard? 5. How many square yards are there in a square whose sides are 3 yd.? 4 yd.? 5 yd.? 5 yd., or a rod? How many square yards are there in a square rod? 6. How many square rods are there in a rectangle 8 rd. by 6 rd.? 10 rd. by 12 rd.? 10 rd. by 16 rd.? A rectangle that contains 160 square rods is called an Acre. 7. How many rods are there in a mile? How many square rods are there in a square whose sides are each a mile, or how many square rods are there in a sq. mi. ? 8. Since there are 160 sq. rd. in an acre, how many acres are there in a square mile? 9. Write out a table of square measures. 24. sq. yd. Reduce to units of lower denominations : 20. sq. rd. 22. sq. rd. 21..625 A. 28. Reduce SOLUTION. 29. Reduce 23..545 sq. rd. 25. .875 sq. ft. 27..495 A. of a sq. yd. to the fraction of a sq. rd. 1 sq. yd. = 11 sq. rd. 20 sq. yd. = of 11 sq. rd. = 8247 sq. rd. of a sq. ft. to the fraction of a sq. rd. 30. Reduce of a sq. in. to the fraction of a sq. yd. 31. Reduce .65 of a sq. yd. to the fraction of an A. 32. Reduce 5 sq. ft. 100 sq. in. to the decimal of a sq. yd. STAND. AR.- - 12 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. 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, 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; the product will then express the volume in cubic units of the same name. 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 cubic foot? 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. ? 7. How many ch. in 20 rd.? In 3 rd.? In 4 rd.? In 32 rd.? In 40 rd.? 23. Reduce 28 links to a fraction of a chain. |