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PROBLEMS.

I. To find the surface of a sphere.

The surface of a sphere is equal to the product of the circumference and diameter.

7 X D X D = surface. (Geometry.) COR-The surfaces of spheres are to each other as the squares of their diameters.

EXAMPLES.

What is the surface of a sphere whose diameter is 3 ft. ?

Circumference = 3.1416 x 3. Surface = 3.1416 x3 x3 = 28.2744 sq. ft. II. To find the volume of a sphere.

The product of the surface and the radius or f the diameter. 7 = 3.1414 and D = diameter.

D
Volume = " X D X D X = .5236 x D3.

6 The volume of a sphere is equal to the cube of the diameter multiplied by .5236.

COR.—The volumes of spheres are to each other as the cubes of their diameters.

EXAMPLES.

1. What is the volume of a sphere whose diameter is 2 feet ? .5236 x 8 = 4.1888 cu. ft. 2. How

many
shot to of an inch in diameter

may

be made of a ball of lead 6 inches in diameter ? 6 x 6 x 6

= 6 x 6 x 6 x 16 x 16 x 16 = 884736 shot. to x 16 xto

a

ANSWERS NOT GIVEN.

IN THE PRECEDING PAGES.

ADDITION AND SUBTRACTION.

Page 18. 1. 3 remain in first field, and there are then 12 in the second.

2. 115 remain in first field, and there are then 977 in the second. 3. $2365. 4. $323.

5. $27586.

Page 19.

6. $57.
7. $5220.
8. Lost $194,

9. $379.
10. $175321.
11. $36.

12. 36311 yds.
13. $131179.

MULTIPLICATION.

1. 18796796. 2. 12895164.

Page 25. 3. 32671178. 4. 17600100.

5. 505489116. 6. 3515971700.

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Page 32.
25. 20 acres. 29. 10 heads. 32. $52239.
26. 15 years.

30. 8 acres. 33. $966.
27. $2.

31. $247640 to grandson.
28. ' 25 rows.
34. Carriage, $513; $63 more than the horses.

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Page 38. 17. 51 = 3, 17.

30.70 = 2, 5, 7.

= 18. 52 = 2, 2, 13. 31. 72 = 2, 2, 2, 3, 3. 19. 54 =

54 = 2, 3, 3, 3. 32. 74 = 2, 37. 20. 55 = 5, 11.

33. 75 = 3, 5, 5. 21. 56 = 2, 2, 2,7.

. 34. 76 =

76 = 2, 2, 19. 22. 57 = 57 = 3, 19.

35. 77 = 7, 11. 23. 58 = 2, 29.

36. 78 = 2, 3, 13. 24. 60 = 2, 2, 3, 5. 37. 80 = 2, 2, 2, 2, 5. 25. 62 = 2, 31.

38. 81 = 3, 3, 3, 3.

3 26. 63 63 = 3, 3, 7.

39. 82 =

82 = 2, 41. 27. 64 = 2, 2, 2, 2, 2, 2. 40.84 = 2, 2, 3, 7. 28. 65 = 5, 13.

41. 85 = 5, 17. 29. 68 = 2, 2, 17. 42. 86 = 2, 43.

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Page 54. 9. 20621..

12. 44187151 . 10. 124676 = 344546 13. 14912634 11. 5202 1.

Page 57. 3. 152. 4. 202.

-5. 1.

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Page 66. Observe that in the first example, 1 is a factor of each product; hence the product is the same as the other factor.

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