1. These men have contracted to paper this house. The rooms are 16' x 14', 12' x 8', 18' x 15', 12' x 10', 15' x 13', 16' x 16', 10' x 6', and 12' x 12'. They deduct 50' from the combined perimeters of the rooms and allow one roll of paper for every 3 ft. How many rolls do they need?

2. A contractor builds a brick wall 68 ft. 8 in. long, 5 ft. 8 in. high, and 2 bricks thick. Allowing 14 bricks per square foot of outside surface for a 2-brick wall, how much will the bricks cost at $8.50 per M?

3. A man has a contract to put up the four walls of a building 80 ft. long, 35 ft. wide, and 78 ft. high. The walls are to be 18 in. thick, and 750 cu. ft. is to be allowed for openings. Allowing 22 bricks to a cubic foot, how much will the bricks cost at $9.25 per M?

4. A contractor wishes to build a concrete wall 66' x 8', and 18" thick. Concrete is Portland cement, which costs $1.90 a barrel of 400 lb., and the rest is gravel costing delivered 87 a load (cubic yard). A cubic foot of dry cement weighs 150 lb. What will the materials cost?

EXERCISE 100

PROBLEMS OF THE FARM

1. A man had 8 acres planted to asparagus. The expense per acre for fertilizers was $40, for labor before cutting $20, for cutting and bunching $40. From each acre he cut 1850 bunches and sold them at 10 a bunch, allowing a commission of 3% for selling. What was his profit from the 8 acres?

2. A farmer, building a barn, orders part of the lumber as follows: 16 pieces of timber 8" x 8", 12 ft. long; 4 pieces 6" x 8", 20 ft. long; 8 pieces 6" x 8", 18. ft. long; 4 pieces 6" x 6", 20 ft. long; 8 pieces 6" x 6", 18 ft. long; and 9 pieces 4" x 6", 12 ft. long. How much will this part of the lumber cost at $26 per M?

3. A poultry raiser paid out for food for 350 hens during the first four weeks of December $30.05. He sold 732 eggs @ 29 a dozen during the first two weeks, 564 eggs @36g a dozen during the third week, and 648 eggs @ 31¢ a dozen the fourth week. His receipts were what per cent greater than the cost of the feed?

4. A farmer spent on a 10-acre field the following sums: plowing, $25; harrowing and rolling, $18.50; seed, $15.50; drilling, $2.75; cutting and threshing, $26.50. His income from the field was 220 bu. of wheat @ 75¢ a bushel, and $3.25 for pasturage. Find the balance in his favor.

5. A farmer is planning to build a poultry house for 350 fowls. He estimates the average weight per fowl to be 6 lb., and he allows 10 cu. ft. of space to each pound of fowl. The house is to be 210 ft. long, 16 ft. wide, and 5 ft. high to the eaves. How high must be the ridgepole in order to give the required capacity?

EXERCISE 101

WORKSHOP PROBLEMS

1. How much will 275 cu. in. of steel weigh, if 1 cu. ft. weighs 490 lb. ?

2. What is the weight of a circular piece of steel shafting 3 in. in diameter and 20 ft. long, 1 cu. ft. of steel weighing 490 lb. ?

3. If the pressure of steam in a boiler is 140 lb. to the square inch, find the pressure on a valve 27 in. in diameter.

4. A boiler contains 480 smoke tubes, each 23 in. in internal diameter. Find the total area for draft through them.

5. If a pressure of 120 lb. to the square inch is applied to the circular plunger of a cylinder 2 ft. in diameter, what is the total pressure ?

6. The rim of a fly wheel contains 1.56 cu. ft. of cast iron when it is 8 in. wide. If the rim were made a foot wide, how much would it weigh, 1 cu. ft. of cast iron weighing 450 lb. ?

7. Out of a rectangular sheet of steel which is 14' 3" long, 3′ 31" wide, and " thick, a circular plate 13" in diameter is cut. If 1 cu. ft. of steel weighs 490 lb., what is the weight of the part of the sheet that is left?

8. If the drive wheel of an engine makes 140 revolutions a minute, and the cylinder is 9 in. in diameter and 14 in. long, and is filled with steam twice in each revolution, how many cubic feet of steam are used in a minute?

9. A hollow steel shaft has an external radius of 9" and an internal radius of 5". If 1 cu. ft. of steel weighs 490 lb., find the weight of 10 ft. of this shaft.

EXERCISE 102

PROBLEMS IN TRANSPORTATION

1. If a freight car is 36 ft. long, 8 ft. 3 in. wide, and 7 ft. 6 in. high, inside measure, how many cubic feet does it contain?

2. In shipping certain goods at the rate of 971 per hundred pounds, there is allowed a discount of 15%. What is the net rate, to the nearest half cent?

3. In shipping certain goods the net rate after deducting 15% from the usual rate for that class is 34 per hundred pounds. What is the usual rate?

4. If a wooden coal car can carry 80,000 lb., and a steel car 100,000 lb., the steel car can carry what per cent more than the wooden car? The wooden car can carry what per cent less than the steel car?

5. A car 36 ft. long and 8 ft. 4 in. wide is loaded with wheat to a depth of 4 ft. 6 in. Reckoning a bushel as containing 1 cu. ft., and a bushel of wheat as weighing 60 lb., how many pounds does the wheat weigh?

6. If the car of Ex. 5 has a capacity of 80,000 lb., to what depth must it be filled with wheat to contain exactly this amount?

7. If a locomotive weighing 115 tons can exert a pull of 221% of its weight in starting a train, how many pounds of pull does it exert ?

8. If a locomotive and coal tender together weigh 95 tons, and there are seven cars to the train, averaging 21 tons each, and a horizontal pull 0.5% of the total weight of the train is required to maintain the necessary speed on a level track, what is this pull in pounds?

1. From the eaves to the ridge of this roof is 13 ft., and the span is 24 ft. What is the rise of the roof?

2. The span of a common A-shaped roof is 26 ft., and the rise of the roof is 6 ft. What is the distance from the eaves to the ridge? (Two decimal places.)

3. A semicircular arch over a door has a span of 4' 8". Required the length of this semicircumference.

4. A builder is putting in a steam pipe 140 ft. long and 2 in. in diameter. What is the radiating surface (that is, the lateral surface that gives out heat)?

5. A builder is putting in a hemispherical dome over a tower that is 12 ft. 6 in. in diameter. What is the area of the surface of the dome?

6. The net excavation needed for a city apartment house is to be 85 ft. long, 50 ft. wide, and 7 ft. deep. In addition to this the excavation is to be extended 7 in. beyond each of the four sides, so as to allow space for working. How many loads (cubic yards) of earth must be removed?