WRITTEN EXERCISE Write the description, plot, and find the area: 1. S.E., Sec. 5, T. 3 S., R. 3 W. 2. N.E., Sec. 8, T. 2 N., R. 2 W. 4. S. 3. E. of N.W. 1, Sec. 2, T. 2 N., R. 3 E. 6. E. 7. N.E. 8. S.W. of N.W. 4, Sec. 32, T. 1 S., R. 3 E. 9. N.W. of N.W. 4, Sec. 6, T. 3 N., R. 3 W. 10. How much is this farm worth at $65 an acre: W. of S., Sec. 3, T. 2 N., R. 2 W.? 11. How much is this farm worth at $75 an acre: N.E. of N.E. 4, Sec. 5, T. 2 S., R. 2 E.? 12. Find the area of this farm: S.W., Sec. 10, T. 2 S., R. 2 E. Draw a plan of a township and locate the farm. 13. Find the area of this farm: N., Sec. 6, T. 1 N., R. 1 E. Draw a plan of a township and locate the farm. 14. Mr. Simmons owns the S., N.E. 4, Sec. 3, T. 2 N., R. 3 E. How many rods of fence are needed to inclose it? 15. How far is it from Mr. Taylor's farm, N.W. of N.W. 4, Sec. 16, T. 1 N., R. 3 W., to Mr. Hunt's farm, S.W. of N.W. 1, Sec. 28, T. 1 N., R. 3 W.? Draw the map. mi. long If hay 16. A road running straight through a farm is and 3 rd. wide. How many acres in the road? can be cut from the sides, averaging of the area, and the amount of hay averages 2 tons to the acre and is worth $9.50 a ton, what is gained by attending to this crop? II. MEASURES. PERCENTAGES. PROPORTION VOLUMES ORAL EXERCISE 1. Give the table of dry measure. 3. Give the table of liquid measure. 4. A cellar is 21' x 18', and 9' deep. Express the dimensions in yards; the volume in cubic yards. 5. At 50 ct. a cubic yard, how much will it cost to excavate a cellar containing 126 cu. yd.? 175 cu. yd.? 21' x 18' means 21 ft. by 18 ft. 6′′ × 5′′ means 6 in. by 5 in. 8. How many cubic feet in a room 10' x 12' x 9'? Find the volumes of solids of the following dimensions: 50. Illustrative problem. What is the volume of a box 3 ft. wide, 6 ft. long, 2 ft. high? If it were 1 ft. each way, the volume would be 1 cu. ft. But it is 3 times as wide, 6 times as long, and 2 times as high. Therefore the volume is 3 times 6 times 2 times 1 cu. ft., or 38 cu. ft. If there is any difficulty in understanding this fact, in this review, inch cubes may be used as in the earlier classes. WRITTEN EXERCISE 1. How many cords in a pile of 4-ft. wood, 5 ft. high and 56 ft. long? 6 ft. high and 128 ft. long? 2. How many loads (cubic yards) of earth must be taken out in excavating a cellar 24' x 18', and 7' deep? 3. How much will it cost to excavate a ditch 150' × 2' × 6', at 50 per cubic yard? at 62 per cubic yard? 4. A schoolroom is 32 ft. 8 in. long, 183 ft. wide, and 12 ft. high. What is the number of cubic feet in the room? 5. A tunnel 720 ft. long has a cross-section area of 180 sq. ft. How much earth and rock were excavated? (Imagine the cross section 10' x 18'.) 6. In preparing a flower bed in a park it was necessary to fill in a space 60' x 100' to an average depth of 11⁄2'. The earth cost 331 a load. What was the total cost of the earth used? 7. A freight car is 8' x 34', and the interior is 7' high. How many cubic feet does it contain? If it is filled with grain to a height of 5', what is the weight of the grain at 60 lb. to the bushel, allowing 11 cu. ft. to the bushel? 8. A fish pond has been excavated to a depth of 5 ft. The dimensions of the bottom are 40 ft. and 30 ft. How much earth was excavated? 9. The size of an ordinary Nebraska farm-wagon box is 10 ft. by 3 ft., and 24 in. to 26 in. deep. Find the contents in cubic feet for each of these depths; also in cubic inches. 10. Such a wagon box 24 in. deep contains 50 bu. of shelled corn. How many bushels of shelled corn will such a box 26 in. deep contain? 11. If a wagon box contains 50 bu. of wheat worth 89¢ a bushel, how many loads must be drawn to carry $311.50 worth? to carry $133.50 worth? 12. Prairie hay is heavier than eastern meadow hay, a cube of the former 7 ft. on an edge weighing a ton (the measurement taken 30 days after the hay is stacked). If it takes 33% more in bulk of a certain eastern meadow hay to make a ton, how many cubic feet to a ton of the latter? 13. What is the weight of prairie hay that will fill a space 30 ft. long, 17 ft. 6 in. wide, and 11 ft. deep, taking the number of cubic feet to the ton suggested in Ex. 12? 14. What is the weight of the eastern meadow hay mentioned in Ex. 12 required to fill the space mentioned in Ex. 13? 15. A haystack is estimated to contain 2600 cu. ft. If prairie hay, what does it weigh, to the nearest half ton? If eastern meadow hay (Ex. 12)? 16. A schoolroom is 30 ft. long, 20 ft. wide, and 15 ft. high. If it is occupied by 29 children and the teacher, how many cubic feet of air are allowed to each? If 2400 cu. ft. of fresh air per hour should be allowed to each person, how many times an hour should the air be changed? PROBLEMS IN EXCAVATION WRITTEN EXERCISE 1. How many cubic yards of earth must be removed in digging a tunnel 492 ft. long, 39 ft. wide, and 19 ft. 6 in. high? 2. If a dirt car is 27 ft. long, 6 ft. wide, and 31 ft. deep, how many cubic yards will it carry? How many will 12 cars carry? 3. If one laborer can shovel a cubic yard of earth into a car in 30 min., how long will it take him to load a car? How long will it take 15 men? (See Ex. 2.) 4. How many cars of the above dimensions will it take to remove the earth from the tunnel mentioned in Ex. 1? How many trains of 9 cars each? Allowing 30 ft. for the total length of a car, how long a train of cars would be needed? 5. If one laborer can remove the earth from a space 20 ft. long, 6 ft. wide, and 6 ft. deep in a day, how long will it take 100 men to remove the earth from the tunnel above mentioned? 6. If a laborer is paid at the rate of 10g a load (cubic yard) of earth removed, what will he earn in a day, removing the amount specified in Ex. 5? 7. In the first great subway in New York City 9733 cu. yd. of brick were used. Taking the size of the brick as 81" × 4′′ × 2", how many bricks were used? 8. What will be the earnings of a laborer who can excavate a space a yard wide, a yard deep, and 12 ft. long, in solid rock, in one day, at 75¢ per cubic yard? How much at 87 per cubic yard? |