CUBIC MEASURE.

121. Cubic Measure is used in estimating the contents of solids; as, wood, masonry, the capacity of cellars, cisterns, &c.

NOTE.99 quarter cubic feet make 1 perch of stone.

ANAL. STEPS.-(1.) Find the number of rows of cu. ft. in 1 cu. yd.

ANALYSIS. Since there are 3 rows of cubic feet in 1 tier of feet,

in 3 tiers, there are 3 times 3 rows, which is 9 rows.

(2.) Find the number of cubic feet in 1 cubic yard.

ANALYSIS.

- Since in 1 row there are 3 cubic feet, in 9 rows, there

are 9 times 3 cubic feet, which is 27 cubic feet.

122. To find the solid contents of a body, we have the following

RULE.-Multiply the length by the breadth, and that product by the thickness.

NOTES. - (1.) A load of earth contains a cubic yard, and weighs about 3250 pounds. A cubic foot of water weighs 621⁄2 pounds.

(2.) Railway and transportation companies estimate light freight by the number of cubic feet it occupies; but heavy freight is estimated by weight.

(3). A pile of wood 4 feet wide, 4 feet high, and 8 feet long, contains 1 cord; and a cord-foot is 1 foot in length of such a pile.

(4.) A brick is usually 8 inches long, 4 inches wide, and 24 inches thick.

(5.) Sawed lumber, as joists, plank, and scantlings, are now generally bought and sold by board measure. The dimensions of a foot of board measure are 1 foot long, 1 foot wide, and 1 inch thick. Thus a plank 12 feet long, 1 foot wide, and 2 inches thick, contains 24 feet board measure, or as much as two boards of the same length and breadth, and 1 inch thick. But boards that are less than 1 inch thick are measured as if they were an inch thick.

ORAL EXERCISES.

1. How many cubic feet in 2 cubic yards?

ANALYSIS. Since in 1 cubic yard there are 27 cubic feet, in 2 cubic yards, there are 2 times as many; or, 54 cubic feet.

2. How many cubic inches in 1 cubic foot and 19 cubic inches?

3. How many cubic feet in 2 cords of wood?

4. How many cubic feet in 1 cord and 17 cubic feet? 5. How many perch of stone in 99 cubic feet?

REVIEW. Give the use of the parenthesis. (39.) Define multiplication. (40.) The multiplicand. (41.) The multiplier. (42.) The product. (43.) Which are factors? (44.) Describe the sign of multiplication, and illustrate its use. (45.) Give the axiom. (46.) Give the principles. (47.)

6. How many cubic inch blocks will it take to fill a mortise one foot long, 3 inches wide, and 6 inches deep?

7. How many quarter cubic inch blocks will it take to fill a mortise one inch each way? One foot each way?

8. How many cubic feet in a block of stone 5 feet long, 3 feet wide, and 3 feet thick?

8. What is the difference in volume between a cube 5 inches on each edge, and 5 cubic inches?

In the above illustration will be seen a part of the walls and foundation of a building 20 feet long, 12 feet wide, and 10 feet high, the walls being 2 feet thick.

WRITTEN EXERCISES.

65. How many cubic feet in the left-hand wall?

FORMULA (1.) 12 cubic feet X 2 = 24 cubic feet.

(2.) 24 cubic feet X 10 240 cubic feet.

ANALYSIS. - (1.) Since in one row (12 feet long) there are 12 cubic feet, in two rows (2 feet thick), there are 2 times as many, or 24 cubic feet.

(2.) Since in 1 tier (12 feet long by 2 feet thick) there are 24 cubic feet, in 10 tiers (10 feet high), there are 10 times as many, or 240 cubic feet.

NOTE. In estimating the contents of walls or masonry, no allowance is made for windows, doorways, or corners. All measurements are understood as being outside measurements, unless otherwise specified.

66. How many cubic feet in the highest side wall?

67. How many cubic feet in the foundation of the lowest end wall? In the foundation of the lowest side wall, making a deduction for the doorway?

68. How many cubic feet in the walls of the building as they now stand?

69. How many cubic feet of masonry will there be in the walls when ten feet high?

70. How many cubic feet of bricks in the pile on the floor of the building?

71. How many cubic feet of bricks will it take to cover the floor inside the walls, one foot thick? How many cubic inches?

72. How many bricks will it take to make the floor one foot thick? What will they cost, at $5 per thousand?

NOTE. - Allowing for mortar, 21 bricks of the common size (8×4 × 24) make a cubic foot.

73. How many bricks will it take to build the walls as they now stand? What will they cost, at $7.30 per thousand?

74. How many bricks will it take to build the walls 10 feet high? How much will it cost, including labor, at $11.20 per thousand?

REVIEW.-Write the analysis of a short example in multiplication. (48.) How may a number be multiplied by 10, 100, 1000, &c? (49.) Give table of U.S. currency. (50.) Give the definition of division. (51) Of dividend (52.) Of divisor. (53). Of quotient. (54.) Of remainder. (55.) Give use of the sign. (56.) Of the frac tional sign. (57.) How does short division differ from long division? (58, 59.)

75. How many perch of stone would be required to make the walls 10 feet high?

SUGGESTION.-Change the cubic feet to quarter cubic feet; then quarter cubic feet to perch.

76. Suppose the walls completed 12 feet high, how many perch of stone would they contain?

77. Suppose the walls to be built 10 feet high, how many cubic feet of wood would it take to fill the inside of the building level with the top?

78. How many cubic inch blocks would it take to fill it?

79. 231 cubic inch blocks are equal in volume to a gallon of water: how many gallons of water will fill a cistern of the same size?

Arrange 128 cubic foot blocks into a pile feet long, 4 feet wide, and 4 feet high, and it will represent the shape and size of a cord. One foot of the length of such a pile is called a cord foot, and contains 16 cubic feet. 8 cord feet make a cord.

REVIEW.-Give the axiom used in division. (60.) Name the principles. (61.) Write the analysis of an example in short division. (62.) How may a number be divided by 10, 100, 1000, &c.? (63.) Write the analysis of a short example in long division. (64.) Give the table of U. S. currency. (65.) Give the table of aliquot parts. (66.) Of what are coins made? (67.) What can you say about the coins? Of what does paper money consist? (68.) What is a bill, or invoice? (69.) Which the debtor? which the creditor? What is an account?