SURFACE MEASURE.

86. A Surface is that which has only length and breadth.

87. The Area of a figure is its quantity of surface.

88. An Angle is the difference in

direction of two straight lines, which meet at a point. Thus, ACD and DCB are angles.

A

B

89. A Square is a surface having four equal sides and four equal angles.

A Rectangle is any surface having four sides and four equal angles.

90. The area of a square, each of whose sides is 1 foot, is 1 square foot.

The area of a rectangle, whose length is 3 feet, and whose width is 2 feet, is 6 square feet; for it is composed of 2 rows of 3 square feet, or of 2 times 3 square feet. Hence,

The area of a rectangle is equal to the product of the length by the breadth.

What is a Surface? The Area of a figure? An Angle? A Square? A Rectangle? To what is the area of a rectangle equal?

91. Surface or Square Measure is used in measuring surfaces.

Table.

144 square inches (sq. in.) are 1 square foot,

9 square feet,

1 square yard,

sq.

sq. ft. yd.

301 square yards,

1 square rod or perch, P.

160 square rods or perches, 640 acres,

1 acre,

A.

1 square mile,

M.

Land is usually measured by Gunter's chain, which is 4 rods, or 66 feet, long, and divided into 100 links, each 79 inches long. 1 square chain is 16 square rods, and 10 square chains are 1 acre. 640 acres make one section of land.

A rood (R.) equals 40 square rods or perches.

MENTAL EXERCISES.

1. How many square inches in 1 square foot?

2. How many square feet in 5 square yards?

3. How many square yards in 1 square rod? In 4 square rods?

4. How many square rods in 2 roods? In 3 roods? 5. How many roods in 5 acres? In 10 acres?

6. How many acres make 1 square mile?

7. How many square yards in 45 square feet? In 81 square feet?

8. How many square rods in 121 square yards?

9. How many roods in 80 square rods? In 120 square rods?

10. How many acres in 16 roods? In 28 roods?

How is the Area of a Rectangle found? For what is Surface Measure used? Recite the Table. How is land usually measured?

SOLID MEASURE.

92. A Solid, or Volume, is that which has length, breadth, and hight or depth.

93. A Cube is a volume bounded by six square and equal sides or faces.

If a cube is 1 yard or 3 feet long, 1 yard or 3 feet wide, and

A Cube.

1 yard or 3 feet high, it is a cubic or solid yard.

94. A Rectangular Solid, or Volume, is any volume bounded by rectangular faces.

In the large cube are represented 3 tiers of small cubes, of 3 rows each, and 3 in a row. If each of these small cubes is supposed to be one cubic foot, then in the large cube there evidently are in one of the equal tiers 3 ́times 3 cubic feet, or 9 cubic feet, and in the 3 tiers, 3 times 9 cubic feet, or 27 cubic feet, or as many as the product of the length, breadth, and hight or depth. Hence,

The contents of a rectangular solid, or volume, are equal to the product of the length, breadth, and hight or depth.

What is a Solid, or Volume? A Cube? A Rectangular Solid? To what are the contents of a Rectangular Solid equal?

95. Solid or Cubic Measure is used in measuring bodies, or things, having length, breadth, and hight or depth.

Table.

1728 cubic inches (cu. in) are 1 cubic foot, cu. ft.

27 cubic feet,

128 cubic feet,

1 cubic yard, cu. yd.

1 cord,

C.

A pile of wood 8 feet long, 4 feet wide, and 4 feet high, is a cord. A cord foot (c. f.) is 1 foot in length of this pile, or 16 cubic feet. A perch of masonry, or of building stone, is 24 cubic feet.

A ton of timber is usually estimated at 40 cubic feet, but as usually measured is about 50 cubic feet.

MENTAL EXERCISES.

1. How many cubic inches in 1 cubic foot?

2. How many cubic feet in 2 cubic yards?

3. How many cubic feet in 2 tons? In 3 tons?

4. How many cubic feet in a cord?

5. How many cubic yards in 54 cubic feet? In 81 cubic feet?

6. How many tons in 80 cubic feet? In 120 cubic feet?

7. How many cord feet in 7 cords? In 9 cords?

8. How many cords in 56 cord feet? In 72 cord feet? 9. How many cubic feet in 3 cubic yards? In 4 cubic yards?

For what is Solid Measure used? Recite the Table. What is a cord of wood? A cord foot? A perch of stone?

The liquid gallon contains 231 cubic inches. Formerly alc, beer, porter, and milk were sold by what was called Beer Measure, and of which the gallon contained 282 cubic inches.

In some States 31 gallons, and in others, 28 to 32 gallons, are considered a barrel.

A hogshead regarded as a measure is 63 gallons.

For what is Liquid Measure used? Recite the Table. How many cubic inches in a liquid gallon? How were beer and milk formerly sold? How many gallons in a barrel? In a hogshead?