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NOTE. Both the length and breadth, if not in units of the same denomination, must be made so, before multiplying.

2. In a floor 16 feet long and 12 feet wide, how many square feet? Ans. 192 sq. ft. 3. How many square yards of carpeting will cover a room 5 yds. long and 4 yds. wide? Ans. 20 sq. yd.

4. How many square yards of carpeting will cover two rooms, one 18 feet long and 12 feet wide, the other 21 feet long and 15 feet wide? Ans. 59 sq. yd.

5. How many square yards in a ceiling 18 feet long and 14 feet wide? Ans. 28 sq. yd. 6. In a field 35 rods long and 32 rods wide, how many acres? Ans. 7 A.

ART. 90. The Area of a Rectangle being equal to the product of the length by the breadth, and as the product of two numbers, divided by either of them, gives the other (Art. 37); therefore,

Rule. If the area of a rectangle be divided by either side, the quotient will be the other side.

ILLUSTRATION.-In Example 1, Art. 89, if the area, 12, be divided by 4, the quotient, 3, is the width; or, divide 12 by 3, the quotient, 4, is the length.

NOTE.-Dividing the area of a rectangle by one of its sides, is really dividing the number of squares in the rectangle by the number of squares on one of its sides. Thus,

In dividing 12 by 4, the latter is not 4 linear inches, but the number of inches in a rectangle 4 in. long and 1 in. wide. See figure, Art. 89.

1. A floor containing 132 square feet, is 11 feet wide: what is its length? Ans. 12 ft.

2. A floor is 18 feet long, and contains 30 square yards: what is its width?

3. A field containing 9 acres, is 45 rods in length: what is its width?

Ans. 15 ft.

Ans. 32 rd.

Ans. 96 rd.

4. A field 35 rods wide, contains 21 acres: what is its - length?

REVIEW.-89. What is the Rule for finding the Area of a Rectangle? 90. The area and one side being given, how may the other side be found?

ART. 91. SOLID OR CUBIC MEASURE:

Used in measuring things having length, breadth, and thickness; as, timber, stone, earth.

ART. 92. A Cube is a SOLID, having 6 equal faces, which are squares. If each side of a cube is 1 inch long, it is called a cubic inch; if each side is 3 feet (1 yard) long, as in the figure, it is a cubic or solid yard.

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The base of a cube, being 1 square yard, contains 3X3=9 square feet; and 1 foot high on this base, contains 9 solid feet; 2 feet high contain 9 X2=18 solid feet; 3 feet high contain 9X3=27 solid feet. Also, it may be shown that 1 solid or cubic foot contains 12X12×12=1728 solid or cubic inches.

Hence, the number of small cubes in any large cube, is equal to the length, breadth, and thickness, multiplied together.

ART. 93. Any solid, whose corners resemble a cube, is a rectangular solid: boxes and cellars are of this form.

The solid contents of a rectangular solid are found, as in the cube, by multiplying together the length, breadth, and thickness.

TABLE.

1728 cubic inches (cu. in.) make 1 cubic foot, marked cu. ft. 27 cubic feet

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40 feet of round or

50 feet of hewn timber}

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128 cubic feet 8X4X4-8 ft.

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1 cubic yard,.

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cu.yd.

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C.

long, 4 ft. wide, and 4ft. high.} 1 cord,

NOTE.-A cord foot, is 1 foot in length of the pile which makes a cord. It is 4 feet wide, 4 feet high, and 1 foot long; hence, it contains 16 cubic feet, and 8 cord feet make 1 cord.

1. Reduce 2 cu.)
2. 28 cords of wood to cu.ft.

.yd. to cubic inches.

Ans. 93312 cu. in.
Ans. 3584 cu. ft.

REVIEW.-91. For what is Cubic Measure used? 92. What is a cube? A cubic inch? Cubic yard? How many sq. ft. in one side of a cubio yard? How many cubic feet in a solid 3 ft. long, 8 ft. wide, and 1 ft. thick? If 2 ft. thick? If 3 ft. thick?

Ans. 272 C. ft.

Ans. 221184 cu. in.

3. Reduce 34 cord of wood to C. ft.
4. 1 cord of wood to cu. in.
5. 63936 cu. in. to cu. yd.

Ans. 1 cu. yd. 10 cu. ft.

6. 492480 cu. in. to tn, round timber. Ans. 7 tn. 5 cu. ft. 7. How many cubic feet in a rectangular solid, 8 ft. long, 5 ft. wide, 4 ft. thick? See Art. 93. Ans. 160 cu. ft. 8. How many cubic yards of excavation in a cellar 8 yd. long, 5 yd. wide, 2 yd. deep? Ans. 80 cu. yd.

9. How many cubic yards in a cellar, 18 feet long, 15 feet wide, 7 feet deep? Ans. 70 cu. yd. 10. In a pile of wood 40 feet long, 12 feet wide, and 8 feet high, how many cords?

ART. 94. CLOTH MEASURE

Ans. 30 C.

Is used in measuring cloth, muslin, ribbons, tape, &c.

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This is a species of long measure, the yard being 36 inches in both.

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Reduce the yards to quarters; then the quarters to Ells Flem.

REVIEW.-92. To what is the number of small cubes in any large cube equal? 93. What is a rectangular solid? How is the solid contents found? Repeat the Table. 94. For what is Cloth Measure used? Repeat the Table. Of what is Cloth Measure a species?

ART. 91. SOLID OR CUBIC MEASURE:

Used in measuring things having length, breadth, and thickness; as, timber, stone, earth.

ART. 92. A Cube is a SOLID, having 6 equal faces, which are squares. If each side of a cube is 1 inch long, it is called a cubic inch; if each side is 3 feet (1 yard) long, as in the figure, it is a cubic or solid yard.

[graphic]

3 feet wide.

The base of a cube, being 1 square yard, contains 3X3=9 square feet; and 1 foot high on this base, contains 9 solid feet; 2 feet high contain 9X2=18 solid feet; 3 feet high contain 9X3=27 solid feet. Also, it may be shown that 1 solid or cubic foot contains 12X12X12=1728 solid or cubic inches.

Hence, the number of small cubes in any large cube, is equal to the length, breadth, and thickness, multiplied together.

ART. 93. Any solid, whose corners resemble a cube, is a rectangular solid: boxes and cellars are of this form.

The solid contents of a rectangular solid are found, as in the cube, by multiplying together the length, breadth, and thickness.

TABLE.

1728 cubic inches (cu. in.) make 1 cubic foot, marked cu. ft. 27 cubic feet

40 feet of round or

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1 cubic yard,.

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cu.yd.

50 feet of hewn timber

128 cubic feet 8X4X4-8 ft.

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C.

long, 4 ft. wide, and 4ft. high. 1 cord,

NOTE.-A cord foot, is 1 foot in length of the pile which makes a cord.

It is 4 feet wide, 4 feet high, and 1 foot long; hence,

feet, and 8 cord feet make 1 cord.

1. Reduce 2 cu. yd. to cubic inches.

2.

28 cords of wood to cu. ft.

contains 16 cubic

Ans. 93312 cu. in.
Ans. 3584 cu. ft.

REVIEW.-91. For what is Cubic Measure used? 92. What is a cube? A cubic inch? Cubic yard? How many sq. ft. in one side of a cubic yard? How many cubic feet in a solid 3 ft. long, 8 ft. wide, and 1 ft. thick? If 2 ft. thick? If 3 ft. thick?

3. Reduce 34 cord of wood to C. ft.

4. 1 cord of wood to cu. in.

5. 63936 cu. in. to cu.

6.

yd.

Ans. 272 C. ft.

Ans. 221184 cu. in.

Ans. 1 cu. yd. 10 cu. ft. 492480 cu. in. to tn. round timber. Ans. 7 tn. 5 cu. ft. 7. How many cubic feet in a rectangular solid, 8 ft. long, 5 ft. wide, 4 ft. thick? See Art. 93. Ans. 160 cu. ft. 8. How many cubic yards of excavation in a cellar 8 yd. long, 5 yd. wide, 2 yd. deep? Ans. 80 cu. yd.

9. How many cubic yards in a cellar, 18 feet long, 15 feet wide, 7 feet deep? Ans. 70 cu. yd. 10. In a pile of wood 40 feet long, 12 feet wide, and 8 feet high, how many cords?

ART. 94. CLOTH MEASURE

Ans. 30 C.

Is used in measuring cloth, muslin, ribbons, tape, &c.

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This is a species of long measure, the yard being 36 inches in both.

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Reduce the yards to quarters; then the quarters to Ells Flem.

REVIEW.-92. To what is the number of small cubes in any large cube equal? 93. What is a rectangular solid? How is the solid contents found? Repeat the Table. 94. For what is Cloth Measure used? Repeat the Table. Of what is Cloth Measure a species ?

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