223. A Rectangular Volume is a body bounded by six rectangles.

The Dimensions of a rectangular volume are its length, breadth, and thickness.

A Rectangular Volume.

224. The Contents of a rectangular volume are the space contained within its bounding surfaces.

The dimensions of a rectangular volume determine its contents. Thus,

A rectangular volume 3 inches long, 3 inches wide, and 2 inches thick, contains in one layer 3 rows of 3 cubic inches, or 9 cubic inches, and 2 such layers, or 2 times 3 times 3 cubic inches, contain 18 cubic inches. That is,

The contents of a rectangular volume are equal to the product of its length, breadth, and thickness, taken in the same denomination.

Also,

One of the dimensions of a rectangular solid equals its contents divided by the product of the other two dimensions.

225. A Cylinder is a round body of uniform diameter, whose bases are equal and parallel circles.

The altitude of a cylinder is the straight line joining the centers of the two bases; as the line A B.

A Cylinder.

226. The Contents of a cylinder are equal to the product of the area of the base by the altitude.

The Curved Surface of a cylinder is equal to the product of its circumference and altitude.

WRITTEN EXERCISES.

23. How many cubic feet in a rectangular block 8 feet long, 4 feet 6 inches wide, and 2 feet 3 inches thick?

Solution. 4 ft. 6 in. = ft.; 2 ft. 3 in. the three dimensions, 8 X X = 81 cu. ft. XX † :

24. The contents of a rectangular block 8 feet long and 4 feet wide are 81 cubic feet. What is its thickness?

8 × 41 = 36

81÷ 36 = 21

21 ft. = 2 ft. 3 in.

Solution.

The conter of the block

are the product of its three dimensions. The product of the length and width is 36. The given product of the three dimensions divided by 36 gives for the thickness 24 ft., or 2 ft. 3 in.

25. What are the contents of a trunk 4 feet long, 21 feet wide, and 18 inches deep?

26. How many cubic feet of space in a room whose dimensions are each 10 feet 6 inches?

27. A rectangular cistern, whose length is 133 feet and breadth 6 feet, contains 2944 cubic feet of water. What is the depth of the water?

28. A box is 2 meters long, 15 decimeters wide, and 1 meter deep. What is its capacity?

29. How many cubic yards of earth must be removed in excavating a cellar 60 feet long, 42 feet wide, and 8 feet 6 inches deep?

30. A block is 3 meters long, 2 meters wide, and 1.45 meters thick. What are its contents?

31. A circular well is 32 feet deep and 3 feet in diameter. How many cubic yards does it contain?

32. A roller is 4 feet 6 inches long, and 6 feet 4 inches in circumference. How much surface will it pass over in revolv ing 36 times?

227. A Range of wood 8 feet long, 4 feet wide, and 4 feet high, makes a cord of wood (Art. 171).

A Cord Foot is 1 foot in length of this range, or 16 cubic feet.

WRITTEN EXERCISES.

33. How many cords of wood in a range 32 feet long, 8 feet high, and 4 feet wide?

34. How many cords of 4-foot wood in a range 64 feet long and 4 feet high?

35. A range of 4-foot wood is 28 feet long and 6 feet high. How many I cords does it contain?

36. A range of 4-foot wood is 56 feet long. How high must it be piled to contain 10 cords?

37. Wood is loaded upon a cart in 2 piles, 3 feet 6 inches wide and 4 feet 6 inches high. Allowing the wood to have been cut 4 feet long, how much wood is there on the cart?

38. A shed contains a pile of wood 30 feet long, 16 feet wide, and 12 feet high. What is the value of the wood at $5.25 a

cord?

BOARD MEASURE.

228. A Board Foot is a square foot of board one inch thick; and

12 board feet make 1 cubic foot.

229. Lumber, or sawed timber, as boards, plank, joists, and the like, is estimated in board feet.

Hewn Timber is estimated either in board feet or cubic feet.

In the measurement of lumber, or hewn timber which tapers, half the width or half the thickness of the two ends is taken.

230. To find the contents of a piece of lumber in board feet,

Multiply the product of the length and width taken in feet by the thickness in inches.

NOTE.

Lumber less than an inch thick is measured as if it were an inch thick. In computations, therefore, thickness may be disregarded if an inch or less.

In the measurement of box boards, however, the standard of thickness is of an inch.

WRITTEN EXERCISES.

39. How many board feet in a joist 21 feet 6 inches long, 4 inches wide, and 3 inches thick?

40. How many board feet in a board 16 feet long, 1 foot

6 inches wide, and 2 inch thick?

41. Required the contents in board feet of a plank 20 feet long, 16 inches wide, and 2 inches thick?

42. How many board feet in a piece of hewn timber 20 feet long, 10 inches thick, and whose width tapers from 18 to 16 inches?

43. What will be the cost of 44 spruce joists, each 18 feet long, 9 inches wide, and 3 inches thick, at $23 a thousand feet?

44. What is the value of 18 planks 2 inches thick, 24 feet long, 21 inches wide, at $35 a thousand feet?

MISCELLANEOUS EXERCISES.

45. A rectangular lot containing 9432 square feet has a frontage of 131 feet. What is its other dimension?

46. A wagon 8 feet long and 3 feet wide has wood piled on it 5 feet high. How much is the wood worth at $5.50 a cord ?

47. How many board feet of plank 2 inches thick will be required to cover a platform 30 ft. 6 in. long and 20 ft. wide?

48. What must be paid, at the rate of $40 a thousand feet, for 6 boards 16 feet long, and in width tapering from 28 to 20 inches?

49. A cistern 2.50 meters long, 90 centimeters wide, and 110 centimeters deep, will hold how many hektoliters of water?

50. How many rolls of paper 12 yards long and 1 foot 8 inches wide will be required to paper a room 18 feet long, 12 feet wide, and 9 feet high, no allowance being made for windows and doors?

51. Allowing .8 of a bushel to a cubic foot, how many bushels of corn can be put in a bin whose inside measure is 4 feet long, 3 feet wide, and 4 feet deep?

52. Allowing 7 gallons to a cubic foot, how much will a tank hold whose inside measure is 2 ft. 6 in. long, 2 ft. wide, and 1 ft. 9 in. deep?