20. What will be the cost of the bricks for a pavement 200 ft. long and 9 ft. wide, at $9 a thousand, if it takes 8 bricks for each square foot?

21. A field that contains 80 acres is 128 rds. long. How wide is it?

143. Divisions of the Section of Land.

1. Draw a 2-in. square. Let it represent a section of land. How many acres does it represent? Mark the right-hand side "east," the left-hand side "west," the upper "north," and the lower "south." Divide it equally by an east-andwest line, and divide the south half as in the margin. One of these smaller large square? How many squares represent? Which

square represents the S. E. of the section? Which represents the S. W. 1? Study the divisions of the S. E. .

EXERCISES.

144. Draw a square and mark each of the following tracts, and tell how many acres it contains:

1. E. of the section; N. W. . 1.

2. S. of the N. W. .

3. N. E. of the N. W. .

NOTE: The teacher should explain the United States system of surveying public lands, making clear the following facts: What a township is; the number of sections a township usually contains; how the sections are numbered; and how the townships are described.

1. A solid has three dimensions-length, breadth, and thickness.

2. A rectangular solid is a solid bounded by six rectangular surfaces.

The surfaces of a solid are called faces, and the sides of the faces are called edges. How many edges has a rectangular solid? How many corners?

3.

A cube is a rectangular solid having square faces.

4. A cubic inch is a cube whose edges are each one inch long. What is a cubic foot? A cubic yard?

5. The unit of solid measure is a cube whose edges are one unit in length.

6. The volume, or contents, of a solid is the number of units it contains.

146. 1. Draw a square 1 in. on each side. Let this represent one face of a rectangular solid. If this solid is 1 in. thick, how many cubic inches does it contain?

2. Draw a rectangle 2 in. long and 1 in. wide. Let this represent one surface of a rectangular solid. If this solid is 1 in. thick, how many cubic inches does the solid contain? Make it 3 in. long. Now, how many cubic inches does the solid contain? How many if it were 4 in. long? 5 in. long? 7 in. long? 12 in. long?

3. Draw a rectangle 8 in. long and 1 in. wide. How many square inches does it contain? Let this rectangle represent one surface of a rectangular solid 1 in. thick. How many inches does it contain? What kind? Make the rectangle 2 in. wide. How many cubic inches does the solid contain if it is 1 in. thick? How many times 8 cu. in.? Make it 3 in. wide. How many cubic inches does it contain? How many times 8 cu. in.? How many would it contain if it were 4 in. wide? 5 in. wide? How many times 8 cu. in. in each case?

1 in. thick.

If it were

4. Draw a rectangle 6 in. long and 5 in. wide. How many square inches does it contain? Let the rectangle be the face of a rectangular solid How many cubic inches does it contain? 2 in. thick how many cubic inches would it contain? How many times 30 cu. in., if it were 3 in. thick? If it were 5 in. thick? 6 in. thick? 9 in. thick? How many cubic inches in each case?

5. Draw a square 1 ft. on each side. Divide it into square inches. How many does it contain? Let it be one face of a rectangular solid 1 in. thick. How many cubic inches does the solid contain? If the solid were 2 in. thick, how many cubic inches would it contain? How many times 144 cu. in.? How many times 144 cu. in., if it were 3 in. thick? 5 in. thick? 8 in. thick? 12 in. thick? How many cubic inches? What is a solid 12 in. long, 12 in. wide, and 12 in. thick called? How many cubic inches in a cubic foot?

6. How many square feet in a surface 3 ft. long and 3 ft. wide? If the surface is a face of a solid 1 ft. thick, how many cubic feet in the solid? If the solid

were 3 ft. thick, how many cubic feet would it contain?

1728 cubic inches (cu. in.)=1 cubic foot (cu. ft.)
27 cubic feet

=1 cubic yard (cu. yd.)

EXERCISES.

148.

18 cu. ft.?

1. How many cubic feet are there in 9 cu. yds.

EXPLANATION: 9 cu. yds.=9 times 27 cu. ft.=243 cu. ft. 243 cu. ft.+18 cu. ft.=261 cu. ft.

Hence, 9 cu. yds. 18 cu. ft.=261 cu. ft.

2. How many cubic feet are there in 9,876 cu. in.? 1728 cu. in.)9876 cu. in.

5 times, 1236 cu. in. remaining.

EXPLANATION: Since 1,728 cu. in. make 1 cu. ft., in 9,876 cu. in. there are as many cubic feet as there are times 1,728 cu. in. in 9,876 cu. in.; that is, 5 times and 1,236 cu. in. remaining. Hence, 9,876 cu. in. =5 cu. ft. 1,236 cu. in.

How many cubic inches are there in:

3. 23 cu. ft. 1,625 cu. in.?