Ex. 109.

How many feet board measure in :

1. A board 18 ft. long, 6 in. wide, 7 in. thick? 2. A board 16 ft. long, 12 in. wide, 1 in. thick?

3. Forty boards 14 ft. long, 10 in. wide, 1⁄2 in. thick?

4. A stick of square timber 8 in. by 9 in., and 30 ft. long? 5. Six joists, each 3 in. by 4 in., and 11 ft. long?

6. Ten joists, each 6 in. by 4 in., and 14 ft. long?

7. A stick of square timber 10 in. by 12 in., and 36 ft. long?

8. Ten 2-in. planks, each 13 ft. long, 15 in. wide?

9. Thirty 3-in. planks, each 12 ft. long, 10 in. wide?

10. A board 24 ft. long, 23 in. wide at one end, and 17 in. at the other, and 1 in. thick?

HINT. The average width is 23 +17 in

2

in.

11. In a stick of timber 40 ft. long and 15 in. square? 12. Ten 4-in. planks 16 ft. long and 10 in. wide?

MEASURES OF VOLUME.

164. A rectangular solid is a solid bounded by six rectangles.

165. If the rectangles are all squares, the solid is called a cube.

166. In the figure represented in the margin, let the length contain 5, the breadth 3, and the height 7 in.

The base may be divided into square inches; there will be three rows of 5 sq. in. each; in all 15 sq. in. Upon each square inch may be placed a pile of 7 cu. in., so that the solid will contain 15 x 7 cu. in.; that is, 3 x 5 x 7 cu. in.

Hence, to find the volume of a rectangular solid,

Express its length, breadth, and height in the same linear unit; the product of these numbers will express its volume in cubic units of the same name as the linear unit.

UNITS OF VOLUME.

167.

1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.).
1 cubic yard (cu. yd.).

27 cubic feet

The units of volume are cubes of the linear units. Thus, 1728-12%, 27 = 33.

168. In measuring wood, a pile 8 ft. long, 4 ft. wide, and 4 ft. high, is called a cord.

Hence,

1 cord foot (cd. ft.) = 16 cu. ft.

8 cord feet

=

1 cord (cd.).

Ex. 110.

(Oral.)

1. A brick is 2 by 4 by 8 in.

Find its volume.

2. How many cubic feet in 2 cu. yds. ?

3. How many cubic yards in 81 cu. ft.?

4. Twelve cubic feet are what part of a cubic yard? 5. How many cords in 40 cd. ft.? in 16 cd. ft.

6. How many cords in a pile of wood 32 ft. long, 4 ft. wide, and 4 ft. high?

7. How many loads of earth, each 1 cu. yd., must be removed in digging a ditch 21 ft. long, 3 ft. wide, and 3 ft. deep?

8. How many cubic feet in a stick of timber 12 in. wide, 9 in. thick, and 24 ft. long?

9. How many feet board measure in a cubic foot?

10. How many cubic feet in a stick of timber 16 in. wide, 9 in. thick, and 21 ft. long?

Ex. 111.

1. Reduce 15 cu. yds. 13 cu. ft. to cubic inches.

2. Reduce 150,000 cu. in. to cubic yards.

3. Subtract 28 cu. yds. 25 cu. ft. 1500 cu. in. from 47 cu. yds. 13 cu. ft. 1236 cu. in.

4. Multiply 17 cu. yds. 17 cu. ft. 187 cu. in. by 11.

5. Divide 22 cu. yds. 10 cu. ft. 933 cu. in. by 7.

6. How many cubic inches can be cut out of a cubic foot? 7. How many cubic feet of water will a cistern hold whose three dimensions are each 4 ft.?

8. How many cubic inches in a rectangular stone post 3 ft. high, 1 ft. wide, and 1 ft. thick?

9. Find the value of 0.975 of a cubic yard.

10. Reduce 13 cu. ft. 864 cu. in. to the decimal of a cubic

yard.

11. A man bought 52 cu. yds. 18 cu. ft. 984 cu. in. of stone for the cellar of a house, and as much for the cellar of a second house. How much did he buy for both? 12. How many cords of wood in a pile 50 ft. long, 6 ft. high, and 4 ft. wide?

13. How many cords of wood in a pile 42 ft. long, 61 ft. high, and 8 ft. wide?

14. What must be the length of a load of wood that is 4 ft. wide, 5 ft. high, to contain 2 cds.?

15. A cubic foot of wood weighs 20 pounds. Find the weight of 10 boards, each 30 ft. long, 1 ft. wide, and 1 in. thick.

NOTE. The gallon of liquid measure contains 231 cu. in. The bushel of dry measure contains 2150.42 cu. in. Therefore the quart of liquid measure contains 57 cu. in., and the quart of dry measure 67 cu. in.

Ex. 112. (Oral.)

1. How many pints in 16 gi.? in 37 gi.?

2. How many pints in 2 qts.? in 7 qts. 1 pt.?

3. How many quarts in 2 pks.? in 3 pks. 3 qts.?

4. How many quarts in 3 bu.?

5. How many baskets holding 21 pks. each will 10 bu. of apples fill?

6. If a pint of milk cost 4 cts., what will a gallon cost? 7. How many times will a gallon of water fill a half-pint cup?

8. How many pint bottles will be required to hold 5 gals. 2 qts. of cider?

9. If 4 qts. of blueberries cost 32 cts., what will a bushel cost at the same rate?

10. A 2-gal. measure of molasses lacks 3 pts. of being full. What is the molasses worth at 80 cts. a gallon? 11. If a horse eats 4 qts. of corn a day, how many days will a bushel last him?

12. If a quart of berries is worth 10 cts., what is a peck worth?

Ex. 113.

1. Reduce 440 pts. to pecks, and 109 pts. to gallons.

2. Reduce 2024 pts. to bushels.