DRILL TABLE No. 7. (See Supplement, Art. 1.) 310. For additional practice in compound numbers. 166–178. Change C to units of the lowest denomination in the example. 179-191. Change 132,687 B to higher denominations. 192-204. Change A to B. 205–217. Add 0.5784 A to D. 218-230. Change 0.4627 A to B. 244-256. Change the numbers of C to a fraction of the highest. 231-243. Add & A to C. 욕 lower denominations in 257-269. Change D to a decimal of the highest denomination in C (4 places). 270-282. What part of A is D? * Troy. 283-295. Take D from C. 309–321. Divide C by 7. SECTION XII. MENSURATION OF SURFACES AND SOLIDS. Oral Exercises. 311. a. How is the area of any rectangular surface found? (Art. 108.) Illustrate by an example and diagram. b. If the length is given in rods and the width in feet, what must first be done? c. If a board is 1 ft. 6 in. long and 4 in. wide, what is its area in square inches? d. When the area and one dimension of a rectangle are given, how can the other dimension be found? e. What must be the length of a board 8 in. wide to contain 100 sq. in.? f. What must be the width of a floor 12 ft. icng to contain 132 sq. ft.? g. Chinese matting is 36 in. wide. How many square yards are there in a roll 72 ft. long? h. Brussels carpeting is yd. wide. How long must a roll be to contain 60 sq. yd.? 312. . How is the volume of any rectangular solid found? (Art. 115.) Show this by an example. j. When the contents and two dimensions of a rectangular solid are given, how do you find the other dimension? k. What must be the depth of a cistern 4 ft. long and 3 ft. wide to contain 60 cu. ft. of water? 7. What must be the height of a room 20 ft. long and 15 ft. wide to contain 3000 cu. ft. of air? SQUARES AND OTHER RECTANGLES. 313. Examples for Written Work. 1. How many bricks 8 in. long and 4 in. wide, laid flatwise, must be used to build a walk 4 ft. wide and 100 ft. long? 2. What must be paid for a concrete walk 5 rd. long and 5 ft. wide, at 90 per square yard? 3. What is the price of a building lot in Brooklyn 25 ft. wide and 80 ft. deep, at $8 a square foot? What is the value of the land per front foot? 4. How much money will a man be worth who owns a quarter of an acre of land worth 20¢ a foot? 5. My neighbor's garden is 100 ft. square; mine contains 100 sq. ft. What is the difference in size? 6. A and B have each a garden containing 10,000 sq. ft. A's is 200 ft. by 50 ft., and B's is 100 ft. square. C is to fence both at 28 per running foot. How much should A pay? How much should B pay? (Make diagrams of both gardens.) of an acre, is rectangular, What is its depth? 7. A building lot contains and measures on the street 45 ft. 8. A rectangular park contains 17.76 acres and is 310.33 yd. long. What is its breadth? 9. What is the area of the upper surface and sides of a marble slab 3 ft. 3 in. by 2 ft. 2.6 in. and 2.5 in. thick? 10. A map drawn to a scale of one inch to 3 miles, is 5 ft. 2 in. by 3 ft. 7 in. What area in square miles does it represent? 11. How many acres were covered by Machinery Hall at the World's Fair in Chicago, 1893, the main building measuring on the floor 846 ft. by 492 ft., and the annex 550 ft. by 49 ft.? 12. Find the cost for flooring the main building above, at 25¢ per hundred sq. ft. of floor for work, and $12 per thousand sq. ft. for boards, allowing 1 tenth additional stock for waste. GOVERNMENT LANDS. 314. The United States public lands, before being offered for sale, are divided by parallels and meridians into rectangular tracts, called townships, each being as nearly as practicable 6 miles square, or 23040 acres in extent. The lines bounding a township extend due north and south, and east and west, and a line on a parallel of latitude is always established as a base. A line of townships extending north and south is called a range. The ranges are designated by their numbers east or west of the principal meridian, and the townships in each range by their number north or south of the base line. Townships are subdivided into sections 1 mile square, or 640 acres, and sections into half-sections, quarter-sections, half-quarter sections, and quarter-quarter sections or lots. Lots which for any reason are irregular in form are designated as Lot 1, 2, 3, 4, etc., of a particular section. City and village plots are subdivided into blocks, and these again into smaller lots. a. What must be paid for the N.E. quarter of section 11 of a South Dakota township at $3 per acre? 13. Among how many people may a township be divided so that each may receive a quarter-quarter section ? 14. If a speculator buys the northern half of a section of land and sells at various times the N.E. of N.W. 1, the N.W. of N.E. 4, the S.E. 4 of N.W. 4, and the N.E. 4 of N.E. 4, how many acres has he left? Draw a diagram to show what parts of his half-section he has left. 15. A real estate agent bought section 24 of township 2 north, range 8 west, at $5 an acre. He sold the S. section at $7 an acre, the N.E. of N.E. 4 at $8 an acre, the S.E. of N.E. at $7.50 an acre, and the N.E. of N.W. at $6.50 an acre. How many acres did he sell? What part of the section had he left? How much did he gain, valuing the portion he retained at its original cost? TRIANGLES. 315. A plane figure bounded by three straight lines is a triangle. Any side upon which the triangle is supposed to stand, as ac, in the triangle abc, is its base. A line extending from the angle opposite to the base a of the triangle and perpendicular to the base is the height or altitude of the triangle. 316. Every triangle is half a rectangle of the same base and height. Hence the area of a triangle is equal to half the product of the number of units in the base by the number of like units in the height; or as it is often expressed, one half of the base multiplied by the height. a. Draw a triangle 3 inches long and 2 inches high, and show that it is half of a rectangle of the same base and height. b. How many square inches are there in your triangle? |