317. Examples for Written Work.

16. Find the area of triangles having the following dimensions. Give the answers in square feet.

Base 30 ft., height 15 ft.

Base 12 rd., height 14 ft.

Base 12 yd. 2 ft., height 5 yd. 1 ft.

17. What must be the height of a triangle that contains 2250 sq. ft., and whose base is 180 ft. in length?

18. How many square feet are there in a triangular flower bed whose base is 18 ft. and the height 8 ft. 6 in. ?

19. Mary is to crochet a half square breakfast shawl, each of its two equal sides being 14 yd. long. How many square feet will she crochet?

20. Find the surface of an octagonal spire, each of whose eight faces is 19 ft. at the base and 514 ft. high.

CIRCLES.

318. A circle may be considered as made up of triangles the sum of whose bases is the

circumference of the circle and whose height is the radius. Hence the area of a circle equals the product of the circumference by half the radius.

What is the area of a circle

21. Whose circumference is 18.8496 ft. and radius 3 ft. ? 22. Whose circumference is 23.562 ft. and diameter 7 ft.?

319. In every circle the circumference very nearly equals the diameter multiplied v 3.1416. How, then, when one dimension of a circle is given can the other be found?

NOTE.

For many purposes 34 or 22, instead of 3.1416, is accurate enough. Work the examples in this article with the decimal value.

What is the length of the circumference of a circle 23. When the diameter is 2 ft. ? 4 ft. 3 in.?

24. When the radius is 5 in.? 11 yd.?

NOTE. - Draw diagrams to illustrate the following examples:

25. What is the distance around a circular pond that is 100 ft. across?

26. What is the diameter of a circle, the circumference being 100 ft.? 50 rd.?

27. What is the radius of a circle whose circumference is 500 ft.? 12 ft. 9 in.?

Find the area of a circle when

28. The diameter=4 rd.

30. The circumference=560 ft. 31. The circumference

480 ft.

29. The radius -5 ft. 4 in. 32. Over how many square feet can a cow feed when tethered so that her head reaches 20 ft. from the stake?

33. The trunk of the largest tree now standing in Califormia has a circumference of 106 ft. What is the distance through and what is the area of a cross section?

34. How many feet of surface has a circular mirror inside a frame which has a breadth of 4 in., and whose outside elge is the circumference of a circle whose diameter is 4. ft. 5 in.?

35 How many square feet are there in the frame of the above mirror?

320. RECTANGULAR SOLIDS.

36. How many cubic inches are there in a block of marble 1 ft. long, 8 in. wide, and 5 in. thick, and what is its weight at 0.098 of a pound to the cubic inch?

37. What is the weight of a block of granite 8 ft. long, 1 ft. wide, and 14 ft. thick, at 165 lb. to the cubic foot? 3. What must be the length of a beam 16 in. by 22 in. to contain 115 cu. ft. ?

39. How many cubic yards of earth must be removed in digging a cellar 20 ft. long, 18 ft. wide, and 10 ft. deep?

WOOD MEASURE.

321. Wood is usually cut for marketing into 4 feet sticks. Two lengths of such wood piled 4 ft. high and 4 ft. wide contain how many cubic feet?

128 cu. ft. is a cord (cd.), used principally in measuring wood. 16 cu. ft., or of a cord, is a cord foot (cd. ft.).

The following illustration represents 1 cd. and 1 cd. ft.

Examples for Oral and Written Work.

322. a. How many cords of seaweed are in a pile 4 ft. high, 4 ft. wide, and 16 ft. long? 20 ft. long? 40 ft. long? b. At $6 a cord for wood, what is the cost of 4 cd. ft.? of 12 cd. ft. ? of 6 cd. ft.?

At $4 a cord for wood, find the cost of a load measuring

c. 4 ft. by 4 ft. by 4 ft.

d. 4 ft. by 4 ft. by 2 ft.

e. 8 ft. by 4 ft. by 1 ft.

f. 9 ft: by 4 ft. by 4 ft.

40. What is the cost at $3.50 per cord of a load of wood 8 ft. by 4 ft. by 3 ft.? 12 ft. by 6 ft. by 4 ft.?

41. If wood is cut in lengths of 4 ft. and piled 4 ft. high, how long must the pile be to contain a cord?

42. If wood cut 3 ft. 9 in. long was sold for 4 ft. wood, at $5.00 a cord, what deduction should be made in the bill for what was sold for 20 cd.?

LUMBER.

323. The unit of measure for boards, plank, joist, and timber is a square foot one inch in thickness called a board foot.

NOTE.

Unless otherwise specified, all square lumber is reckoned s at least 1 in. thick; all over 1 in. to 1 in. as 1 in.; all over 1 to 11⁄2 in. as 11⁄2 in.; all over 11⁄2 in. to 2 in. as 2 in.; all over 2 in., according to its thickness. Thus, a plank 20 ft. long, 9 in. wide, and 2 in. thick contains 20 × 1 × 2 = 30 board feet.

12

Give the contents of the following lumber in board feet:

43. 3 boards 12. ft. by 12 in. 44. 2 boards 16 ft. by 6 in. 45. 6 boards 14 ft. by 8 in.

46. A 2 in. plank 16 ft. by 8 in. 47. Joist 20 ft. by 6 in. by 6 in. 48. Joist 30 ft. by 6 in. by 4 in.

49. Scantling 100 ft. by 3 in. by 2 in. 50. Scantling 75 ft. by 3 in. by 3 in. 51. Find the cost of boards

of an inch thick required to

lay a platform 75 ft. by 48 ft., at $18 per M. (thousand ft.).

What is the cost of the following lots of square timber:

52. 200 ft. 8 in. by 6 in., at $20 per M.?

53. 450 ft. 10 in. by 12 in., at $24 per M.? 54. 285 ft. 14 in. by 14 in., at $30 per M.? 55. 56 ft. 16 in. by 16 in., at $22 per M.?

56. How many feet are there in 12 boards, each 14 ft. long, 15 in. wide at one end, and 11 in. wide at the other? NOTE. - For the width take the average of 15 in. + 11 in.

57. How many feet has a plank 20 ft. long and 2 in. thick, 14 in. wide at one end and 9 in. wide at the other? 58. What will be the cost of a pine plank 20 ft. long, 30 in. wide, 2 in. thick, at $45 per M.?

59. An unfinished stone tower 271 ft. by 271 ft. was provided with a temporary roof, the four sides ending in a point 15 ft. from their bases. How many board feet would be required for the roof, not allowing for waste?

LATHS, SHINGLES, AND CLAPBOARDS.

324. Laths are 4 ft. long, 1 in. wide, and are usually laid in. apart at the sides, and close together at the ends.

60. How many square yards will be laid by a bundle of 100 laths?

61. How many bundles, 100 laths each, will be required to lath a ceiling 16 ft. by 15 ft. ?

325. Shingles are 16 in. long and of various widths, but in reckoning, each width of 4 in. is considered one shingle; a bundle contains 250 shingles. Shingles are ordinarily laid from to to the weather.

NOTE. - A shingle 16 in. long, laid } to the weather is 5 in. to the weather, and therefore covers 5 in. × 4 in. of surface. A shingle

16 in. long laid to the weather covers 4 in. x 4 in. of surface.

62. When shingles are laid 4 in. to the weather, how many shingles will cover the two sides of a roof each 40 ft. long and 25 ft. wide?

63. How many square feet of surface will 1000 shingles cover when laid to the weather? How many square feet will they cover if laid to the weather?

64. When 1 bundle of shingles is allowed for 30 sq. ft., how many bundles will be required for a roof 20 ft. long and 18 ft. wide, and what will they cost at $2.50 a thousand?

326. Clapboards are sometimes cut 4 ft. long and fin. wide, and sold in bundles of 25 each.

65. When clapboards are laid 31⁄2 inches to the weather, how many square feet will 6 bundles cover?

66. How many clapboards laid 31 in. to the weather will be required to cover 140 sq. ft. ?

67. How many will be required to cover the side of a house 40 ft. long and 20 ft. high?