APPROXIMATE MEASUREMENTS

Approximate equivalents of the following measures are:

1 bu. shelled grains

=

11 cu. ft.

1 bu. apples, coal, roots, corn in ear, etc. =

15 cu. ft.

1. A water meter registered 900 gallons of water consumed in a month. Estimate the weight of the water used, and its volume in cubic feet.

2. The inside measurement of a wagon box is 12 ft. 4 in. by 3 ft. 6 in. by 16 in. Estimate the number of tons, etc., of anthracite coal it would contain; the number of tons, etc., of soft coal.

3. The rainfall on a roof 20 ft. by 30 ft. during April and May was 9.5 in. Find the weight of the water that fell on the roof during that time.

4. A swimming pool is 80 ft. long, 60 ft. wide, and 5 ft. deep. Estimate the number of barrels of water in the pool.

5. Estimate the number of bushels in an oat bin 14 ft. long and 10 ft. wide if the bin is filled with oats to a depth of 6 feet.

6. How many tons of hard coal are there in a bin 16 ft. x 12 ft., when the pile is 1 ft. high?

7. There are 5 ft. of water in a cistern 4 ft. in diameter. How many gallons of water are there in the cistern?

8. Find the weight of the water in a railroad tank 12 ft. in diameter and 16 ft. in depth, if the tank has 12 ft. of water in it.

9. How many bushels of wheat can be shipped in a car whose inside measurements are 36 ft. by 8 ft. 6 in. by 8 ft. ?

10. Estimate the number of tons of clover hay in a mow 60 ft. by 18 ft. by 16 ft. Estimate the number of tons of timothy hay in the same mow.

REVIEW PROBLEMS

1. A field containing 20 acres is 64 rods long. How wide is it?

2. The area of the floor of a schoolroom contains 1120 sq. ft. The air in the room occupies 16800 cu. ft. What is the height of the ceiling?

3. How many tiles 6 in. square are required for a hall 40 ft. by 20 ft. 6 in.?

4. The side of a square is 20 inches. perimeter.

Find its area; its

5. The edge of a cube is 18 inches. Find its surface; its

contents.

6. How many cubical boxes whose edges are 6 in. can be put into a box 8 ft. 6 in. by 4 ft. 6 in. by 3 ft.?

x

7. How many cakes of soap 2 in. × 2 in. × 4 in. may be packed in a box 2 ft. long, 1 ft. wide, and 1 ft. high?

8. The edges of two cubes are respectively 10 inches and 12 inches. How much more surface has one than the other?

9. Find the cost of a farm, 480 rods long and 320 rods wide, at $60 per acre.

10. How much will it cost to put a wire fence around this farm at 50 per rod?

11. A ranchman bought one square mile of land at $10 per acre. He put a fence around it and then divided it by fences into four equal square farms for his sons. Find the entire cost if the fence cost $.40 per rod.

20°

12'

14'

6'

12. Estimate the contract price of building this cellar wall 18 in. thick and 6 ft. in height at $5.95 a perch, no allowance being made for openings.

13. Estimate the number of bricks necessary for a dwelling erected on the foundation as given in example 12, if the walls are 3 bricks thick and 20 feet in height, making an allowance of 150 square feet for openings.

40'

14. Estimate the cost of the face brick for the above dwelling at $16.50 per thousand and $9.00 per thousand for laying; and the cost of the inside brick at $7.00 and $6.00 per thousand for laying.

15. A level lot 60 ft. by 120 ft. has erected on it a dwelling 36 ft. by 42 ft. If the excavating averages 5 ft. and the removed earth is placed on the lot, to what height will it raise the grade of the lot?

16. A certain town has a cylindrical water tank 20 ft. in diameter and 45 ft. in height. The gauge shows 30 ft. of water in the tank. Estimate the weight of the water in the tank.

17. How many yards of carpet, 27 in. wide, are required for a room 24 ft. by 20 ft. 3 in.? Strips are to run lengthwise.

18. How much will it cost to carpet a room 24 feet square with carpet 27 inches wide, at $1.25 per yard, allowing 10 inches on each strip except the first for matching?

19. How much will it cost to plaster a room 20 ft. by 16 ft. and 12 ft. to the ceiling, at 20 per square yard, allowing for one door 31 ft. by 7 ft., and 2 windows, each 4 ft. by 6 ft.?

20. This plot of ground is 700 ft. long and 600 ft. wide. Find the cost of grading streets 40 ft. in width run through the center each way, as here shown, at $1.90 per linear yard. Find the amount from the sale of lots 30' × 140' facing on Oak, Center, and Clark Streets, at $20 per front foot.

700 ft.

Oak St.

Center St.

Clark St.

21. Each of the three sides of a triangle is 50 ft. is the size of each of its angles? Draw the figure.

What

22. The sides of a triangle are 80 ft., 80 ft., and 30 ft. respectively. If the angle opposite the short side is 24°, what is the size of each of the other angles? Draw the figure.

23. The angle opposite one of the equal sides of an isosceles triangle is 75°. Find the size of the other two angles. Draw the figure.

24. One angle in a right triangle is 13.75°. Find the

other two.

25. The angle opposite the base in an isosceles triangle is 1810. What is the size of the other two angles?

26. A railroad company owns a strip of land, in the form of a parallel

ogram, 66 ft. wide and 92.78 rd. long through this farm. Find the area of A and the area of the part owned by the railroad. How can the area of B be found?

27. A wheel is 3 ft. in diameter. How many

revolutions will it make in moving forward 942.48 ft.? 28. The speed of a vessel for 5 hours was 23.17 knots per hour. Find her average speed per hour in statute miles.

29. Lead is 11.35 times as heavy as water. value of a cubic foot of lead at 5 per pound.

Find the

30. How many rolls of paper are required for a room 20 ft. × 18 ft. and 13 ft. 3 in. from the top of the baseboard to the ceiling, allowing for 2 windows 3 ft. in width and one door 3 ft. wide (papering the ceiling lengthwise)?

31. The base of a triangle is 30 ft. and its altitude 23 ft. Find its area.

32. A barn is 80 ft. by 50 ft. It is 40 ft. to the base of the gable and 58 ft. to the top of the gable. How much will it cost to paint it at 8 per square yard? &

33. If the slope of the roof of the barn in problem 31 is 32 ft. long, and it projects 1 ft. at each end, how much will it cost to roof it at $8 per square?

34. A schoolroom is 40 ft. long and 30 ft. wide. Estimating 450 cubic feet of air to each person, what should be the height of the room to accommodate 39 pupils and their teacher?