7. 25 sq. yd. to a decimal of an acre.
8. 14 P. to a decimal of a sq. mi.

9. of a sq. mi. to a compound number. 10. .0005 of an A. to sq. feet.

11. § of a Tp. to a compound number.

12. .0008 of a sq. mi. to a compound number.

Find the sum of

13. of an A., § of a sq. rd., and 3 A. 158 sq. rd. 25 sq. yd. 14. of (1 Tp. 18 sq. mi. 584 A.), and of (378 A. 9 sq. ch. 12 P.)

15. Find the difference between ( of 6 sq. mi. + § of an A.), and (of an A. + of a pole).

16. Subtract 1 sq. 1. from 1 acre; from 1 township.

17. A tract of land containing 984 A. 7 sq. ch. 12 P. was divided into 7 equal farms; what was the size of each farm?

What is the area of rectangles of the following dimensions:

18. 15 yd. by 12 yd?

19. 16 yards square?

20. 9 yd. by 18 yd?

21. 7.5 ch. by 3 ch. 8 1?
22. 4 yd. 2 ft. 4 in. by 34 yd?
23. 3.4 yd. by 9

yd?

24. How many square feet of lumber required for the floors of a house containing 2 rooms 15 ft. by 19 ft., 5 rooms 14 ft. by 16 ft., and 3 rooms 12 ft. by 15 ft.? Ans. 2230 sq. ft.

25. How many boards 12 ft. long and 4 in. wide required to floor a room which is 48 ft. by 32 ft.? Ans. 384 boards. 26. How many yards of carpeting 2 ft. 3 in. wide will be required for 3 rooms 18 ft. by 24 ft., and 4 rooms 12 ft. by 16 ft. 6 in.? Ans. 309 yds.

27. Find the cost of carpeting a house containing rooms as follows: 4 rooms 15 ft. by 19 ft. 6 in., carpet yd. wide at $1.26 per yard; 2 rooms 18 ft. by 25 ft., carpet yd. wide at $2.45 per yard; and 5 rooms 12 ft. 8 in. by 16 ft., carpet 1 yd. wide at $1.08.

Ans. $620.

28. Find the cost of glazing 10 windows, each 9 ft. 10 in. by 5 ft. 3 in., at $.94 a square foot.

Ans.

29. How many tiles 10 inches square will lay a floor 32 ft. 5 in. by 23 ft. 6 in.? Ans. 1096.98. 30. How many flag-stones, 3 ft. 5 in. by 2 ft. 6 in. will be required to cover a court 125 ft. by 82 ft., and what will be the cost of flagging the court at $1.87 a square yard?

31. Find the cost of lathing and plastering a house at $.52 per square yard, containing the following rooms, no allowance being made for doors, windows, and baseboard; 3 rooms 14 ft. by 18 ft., and 2 rooms 12 ft. by 15 ft., height of ceiling 11 ft.; 4 rooms 12 ft. by 16 ft., and 2 rooms 12 ft. by 141⁄2 ft., height of ceiling 9 ft. 6 in. Ans.

32. The ridge of the roof of a building is 44 ft. long, and the distance from each eave to the ridge is 19 ft. 3 in. How many shingles 4 in. wide, laid 5 in. to the weather will be required to roof the building, the first row being double ?

33. What will be the cost of papering a room 20 ft. by 32, height of ceiling 12 ft., with rolls of paper 8 yards long 18 inches wide, at $1.63 per roll, deducting 132 sq. ft. for doors, windows, and baseboard?

UNITS OF VOLUME.

408. A Solid or Volume has three dimensions—length, breadth, and thickness.

409. A Rectangular Solid is a body bounded by six rectangles called faces.

410. A Cube is a rectangular solid, bounded by six equal squares.

411. The Unit of Measure is a cube whose edge is a unit of some known length.

412. The Volume, or Solid Contents of a body is

expressed by the number of times it contains a given unit of measure. For example, the contents of a cubic yard is expressed as 27 cubic feet.

Hence, the volume or contents of a cubic yard expressed in cubic feet, is found by taking the product of the numbers denoting its 3 dimensions in feet.

The contents of any rectangular solid is found in the same manner; hence the following

413. RULE.-Find the product of the numbers denoting the three dimensions expressed in the lowest denomination named. This result is the VOLUME, and can be reduced to any required denomination.

To find a required dimension.

414. RULE.-Divide the volume by the product of the numbers denoting the other two dimensions.

The volume, before division, must be reduced to a cubic unit corresponding with the square unit of the product of the two dimensions.

3. Use.-Used in computing the volume or contents of solids.

EXAMPLES

FOR

PRACTICE.

415. Reduce and explain the following:

1. 97 cu. ft. to cu. in.

3. 4 cu. yd. 394 cu. ft. to cu. in.

2. .09 of a cu. yd. to cu. ft. 4. .0007 of a cu. yd. to cu. in.

5. of a cu. ft. to a decimal of a cu. yd.

6. .8 of a cu. ft. to a decimal of a cu. yd.

7. Find the sum of of a cu. yd. and .625 of a cu. ft.

8. Find the difference between of a cu. yd. and .75 of a cu. ft.

Find the contents of rectangular solids of the following dimensions:

9. A solid 24 ft. long by 1 ft. 6 in. by 2 ft. 9 in.

10. A cube whose edge is 3 yd. 2 ft. 8 in.

11. A solid 7 ft. 9 in. long by 3 ft. 4 in. by 4 ft. 6 in.

12. A solid 12 yd. 1 ft. 9 in. long by 2 yd. 2 ft. by 2 ft. 8 in. 13. How many cubic feet in a stick of timber 38 ft. long by 2 ft. 3 in. by 1 ft. 9 in?

14. A cistern 9 ft. square contains 1092 cu. ft.; what is its depth?

15. A stick of square timber contains 189 cu. ft., 2 of its dimensions are 1 ft. 9 in. and 2 ft. 3 in.; what is the other? 16. A bin contains 3261 cu. ft.; 2 of its dimensions are 9 ft. 8 in. and 7 ft. 6 in.: what is the other?

17. How many cubic feet of air in a room 74 ft. 9 in. long, 52 ft. 10 in. wide, and 23 ft. 6 in. high?

18. How many cubic yards of earth in an embankment 283 ft. by 42 ft. 8 in. by 18 ft. 6 in. ?

19. A vat is 7 ft. 2 in. by 4 ft. 9 in. by 3 ft. 4 in. How cubic feet does it contain ?

many

20. In digging a cellar 48 ft. 6 in. by 39 ft. 8 in., and 8 ft. 4 in. deep, how many cubic yards of earth must be removed?

21. What will be the cost of the following bill of square

timber, at $.33 per cubic foot:

(1.) 3 pieces 13 ft. by 9 in. by 7 in. ?

(2.) 8 pieces 15 ft. 6 in. by 10 in. by 8 in. ?

(3.) 4 pieces 23 ft. by 8 in. by 9 in. ?

(4.) 6 pieces 36 ft. by 1 ft. 6 in. by 1 ft. ?

(5.) 9 pieces 18 ft. 9 in. by 1 ft. 3 in. by 9 in.?

(6.) 12 pieces 15 ft. by 7 in. by 91 in.?

22. How many perches in a wall 37 ft. long, 23 ft. 6 in. high, and 2 ft. 6 in. thick?

Table of Units for Measuring Wood and Stone.

= 1 Cord Foot (cd. ft.)) Used for measur

16 cu. ft.

128 cu. ft.

243 cu. ft.

ing both wood and stone.

= 1 perch (pch.) of stone or masonry.

1 cu. yd. of earth is called a load.

1. The materials for masonry are usually estimated by the cord or perch, the work by the perch and cubic foot, also by the square foot and square yard.

2. In estimating the mason work in a building, each wall is measured on the outside and no allowance is ordinarily made for doors, windows, and cornices, unless specified in contract. In estimating the material, the doors, windows, and cornices are deducted.

3. Brickwork is usually estimated by the thousand bricks. The size of a brick varies thus: North River bricks are 8 in. × 3 × 21, Philadelphia and Baltimore bricks are 8 in. × 43 × 28, Milwaukee bricks 8 in. × 43 × 23, and Maine bricks 7 in. × 38 × 28.

4. Excavations and embankments are estimated by the cubic yard.