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37. Of 25 tons of meal at $25 per ton.
38. Of 35 acres of land at $35 per acre.
39. Of 45 M. ft. of lumber at $45 per M
(ii) Find the sum of the three results.

40. Of 23 yd. cloth at 27¢ a yard.
41. Of 36 yd. cloth at 34¢ a yard.
42. Of 42 yd. cloth at 48¢ a yard.

(jj) Find the sum of the three results.

43. Of 3240 ft. lumber at $15 per M.
44. Of 2460 ft. lumber at $15 per M.
45. Of 1620 ft. lumber at $16 per M.
(kk) Find the sum of the three results.

46. Of 99 lb. butter at 23¢ a pound.
47. Of 99 lb. butter at 28¢ a pound.
48. Of 98 lb. butter at 24¢ a pound.

(11) Find the sum of the three results.

49. Paid $15.50 for ribbon at 1634 a yard. How many yards did I buy?

50. Paid $24.75 for ribbon at 1214 a yard. How many yards did I buy?

(mm) Find the sum of the two results.

PRACTICAL APPROXIMATIONS.

So far as practicable, solve the following problems without the aid of a pencil. At least, exercise the judgment on every problem before making any figures.

1. The specific gravity* of iron being about 74, how much does a cubic foot of it weigh? How much does a cubic inch of iron weigh?

2. A 4-inch iron ball weighs about

inch iron ball weighs about

pounds.

pounds. A 2

3. An iron rod, 1 inch in diameter and 12 feet long, weighs about - pounds. An iron rod 2 inches in diameter and 12 feet long weighs about - pounds.

4. A sheet of boiler iron, 8 feet square and 3 of an inch thick, weighs about

pounds.

5. What is the weight of the water that will fill a tank 2 feet wide, 2 feet deep, and 10 feet long?

6. The specific gravity of limestone is about 2. What is the weight of a piece of limestone that is 4 feet square and 3 inches thick ?

7. The specific gravity of seasoned white pine is about .5; that is, a piece of white pine weighs about 5 tenths as much as the same bulk of water weighs. How much does a pine board 1 foot wide, 1 inch thick, and 12 feet long, weigh?

8. What is the weight of a stick of timber 12 inches by 12 inches and 20 feet long, if its specific gravity is .7?

9. What is the weight of 1000 feet of green lumber if its specific gravity is .9 ?

*When we say that the specific gravity of iron is about 71, we mean that it weighs about 71 times as much as water, the same bulk being considered.

10. The specific gravity of sand is about 2. How much does a load (27 cu. ft.) of it weigh?

11. If the specific gravity of granite is 2.7, how much does a cubic yard of it weigh?

12. The specific gravity of brick and mortar is nearly 2. What is the weight of a cubic foot of brick wall?

13. If a brick, 8 in. by 4 in. by 2 in., weighs 4 pounds, is its specific gravity more or less than 2? That is, does 1 cubic foot of bricks weigh more or less than exactly twice as much as 1 cubic foot of water?

14. If the specific gravity of Athens (Illinois) limestone is 2.4, and if a cord of it is equal to 100 solid feet, how much does a cord of this stone weigh?

15. If bricks, 8 in. long, 4 in. wide, and 2 in. thick, are laid on their largest face, how many bricks will be required for a walk 6 feet wide and 100 feet long, making some allowance for imperfect bricks and breakage in handling?

16. What is the capacity in gallons of a tank 5 feet long, 2 feet wide, and 2 feet deep?

17. Give the dimensions of a tank the capacity of which is 225 gallons.

18. A certain cylindrical tank is 8 feet in diameter. Each foot in depth will contain how many gallons?

19. One inch of rain-fall will give how many pounds of water on a horizontal surface 30 feet by 40 feet?

20. Two inches of rain-fall will give how many barrels (31 gal.) of water on a horizontal surface 40 feet by 60 feet?

21. A one inch rain-fall will give how many tons of water to the acre?

22. Your school-house lot is what part of an acre?

23. A one inch rain-fall will give how many barrels (31 gal.) of water on the school-house lot?

24. Your school-room floor is what part of an acre?

25. The distance around your school-room is what part of a mile ?

26. How many bushels of oats would be required to fill your school-room to the depth of 3 feet?

27. A shed as large as your school-room would hold how many cords of wood?

28. Give the dimensions of a crib that will hold 1000 bushels of corn.

29. Give the dimensions of a pile of wood that contains 40 cords.

30. A piece of land 100 feet long and 5 rods wide is what part of an acre?

31. How many cubic inches in a cylinder 8 inches in diameter and 10 inches long?

32. How many cubic inches in an 8-inch sphere?

33. If 468.25 be multiplied by .5106 will the product be more or less than 234 ?*

34. If 484,079 be multiplied by .251, will the product be more or less than 121?.

35. If 2480 be multiplied by .2479 will the product be more or less than 620 ?

36. If 6400 be multiplied by .74, the product will be how many less than 3 of 6400 ?

37. If 4800 be multiplied by 1.6, the product will be how many more than 11⁄2 times 4800?

38. If 366.06 be divided by &, will the quotient be more or less than 366 + 1 of 366 ?

* Observe that 234 is of 468.

39. If 25.2314 be divided by 1, will the quotient be more or less than 51 ?

40. If 250 be divided by .26, will the quotient be more or less than four times 250?

41. If cheese is worth 17 cents a pound, how much should be paid for (a) 2 lb. 3 oz.? (b) 3 lb. 5 oz.? (c) 1 lb. 7 oz.? (d) 4 lb. 9 oz. (e) 2 lb. 11 oz.?

42. If meat is worth 15 cents a pound, how much should be paid for (a) 1 lb. 4 oz.? (b) 2 lb. 6 oz.? (c) 1 lb. 7 oz.? (e) 3 lb. 13 oz.?

(d) 2 lb. 9 oz.?

43. If cheese is worth 12 cents a pound, how much

should be paid for (a) 2

1 oz.? (d) 4 lb. 9 oz.?

lb. 8 oz.? (b) 2 lb. 4 oz.? (c) 3 lb.

(e) 4 lb. 15 oz.?

44. A wagon box 10 feet by 3 feet by 16 inches will contain how many bushels of shelled corn?

45. The surface of a sphere is equal to 4 times the area of a circle having the same diameter as the sphere. How many square inches in the surface of a 10-inch sphere?

46. How many square inches in the surface of a 20-inch. sphere ?

47. If from a cylinder of wood the largest possible cone be cut, exactly 3 of the wood will be cut away. The solid content of a cone is therefore exactly of a cylinder having 1-80 the same base and the same altitude (length). How many cubic inches in a cone the diameter of whose base is 8 inches and whose altitude is 12 inches?

48. How many bushels of grain in a conical pile whose diameter is 6 feet and whose altitude is 4 feet?

49. At 10 cents a square yard, what is the cost of painting the outer surface of a cylindrical standpipe whose diameter is 15 feet and whose altitude is 36 feet?

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