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56. Apply Weddle's Method to find the content of an irregular area by means of seven equidistant ordinates; namely, 5, 9, 15, 20, 19, 17, 14; the distance between the ordinates being 8. Ans. 727 2.

57. Draw a diagram, and calculate the area of the figure from the following offsets taken in yards: at o, 60; at 80, 75; at 120, 56; at 150, 96; at 190, 0.

Ans. 2 a. 2 r. 4 p.

58. Find the value of a square board whose side is 8 ft. 4 in., at 2d. per foot. Ans. 14s. 5 d.

59. The hypothenuse of a right-angled triangle is 4 ft. 5 in., and the base 2 ft. 4 in.; find the perpendicular.

60. The three sides of a triangle are 2 ft. 4 ft. 8 in.; find the area by duodecimals.

Ans. 3 ft. 9 in.

1 in., 3 ft. 3 in.,

Ans. 211 feet.

61. The radius of a circle is 6 feet; find the area of the sector, and the length of the arc, which contains 32°. 15'. Ans. 10 137, 3'379.

62. Find the amount of 73 ft. 9 in. at 151d. per foot. Ans. £4. 15s. 3žd.

63. Find the content of an irregular area from the seven equidistant ordinates 5, 7, 8, 10, 13, 17, 14, yards; the distance between them being 6 yards.

Ans. 396 yards.

64. The diameter of a circle is 30; find the area of a

segment cut off by a chord whose length is 24.

Ans. 99'904.

65. The axis of a parabola is 18, and the base 12; if it be divided into two unequal parts by a line whose length is 10, drawn parallel to the axis, find by means of seven equidistant ordinates the area of the smaller part.

CURVE SURFACES AND SOLIDS.
THE CUBE.

Ans. 103.

XXII.

To find the solidity of a cube.

Cube the edge.

Ex. Find the solidity of a cube whose edge is 3 ft. 2. in.

[blocks in formation]

Note.-Twice the square of the diagonal gives the whole

surface of the cube.

I.

EXAMPLES.

Find the solidity and surface of a cube whose edge is 53 feet.

2.

Solidity, 190. 1.3.9 feet. Surface, 198. 4. 6 feet. Find the solidity and surface of a cube whose edge Solidity, 3941 c. ft. Surface, 322 sq. ft.

is 7 ft. 4 in.

3.

Find the solidity and surface of

is 3 ft. 4 in.

9 in.

a cube whose edge

Solidity, 37 c. ft.

Surface, 663 sq. ft.

7

4. Find the surface of a cube whose diagonal is 6 ft. Ans. 91 sq. ft.

5. Find the surface of a cube whose diagonal is 6 ft. Ans. 79.2.0. 6 feet.

3 in.

6. Find the weight of a cubical block of cast iron whose edge is 15 inches. Ans. 7 cwt. 2 qrs. 32 lbs.

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This solid is bounded by 6 rectangular planes, of which the opposite pairs are equal.

XXIII.

To find the solidity of a parallelopipedon.

Multiply the three contiguous edges together.

Ex. I. Find the solidity of a parallelopipedon whose dimensions are 14, 18, 36 inches.

[blocks in formation]

Ex. 2.

[blocks in formation]

Find the number of gallons contained in a rectangular cistern whose dimensions are 6 ft. 3 in., 4 ft. 4 in., 5 ft. 8 in.

75

52

150

375

3900

68

31200

23400

2,7,7,2,7,4) 2652000 (955 455 galls.

2495466

156534

138637

17897

16636

1261

1109

152

138

14

14

XXIV.

Given the breadth and thickness of a rectangular beam, to find the length when the solidity is given.

Divide the solidity by the product of the length and breadth.

Ex. The breadth and thickness of a beam are 20 and 15 inches; find the length of a piece which contains 10 cubic feet.

10 ÷ (1 × 13) = 10 × × 3 = 4 feet.

EXAMPLES.

I. Find the solidity of a parallelopipedon whose dimensions are 16, 18, 30 inches.

Ans. 5 c. ft.

2. Find the solidity and surface of a parallelopipedon whose dimensions are 6 ft. 3 in., 4 ft. 6 in., 3ft. 9 in.

Solidity, 10515 c. ft. Surface, 1367 sq. ft.

3. Find the number of gallons in a rectangular cistern whose dimensions are 11, 12, 13 yards.

Ans. 552 galls. I pt.

4. The breadth and thickness of a beam are 7 and 5 inches; find what length must be cut off to contain 1967 cubic inches. Ans. 5 inches.

5. The length and breadth of a tank are 60 and 42 feet; find the depth in order that it may contain 840 cubic yards.

Ans. 9 feet.

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