13. Find the cost of covering the floor of a hall 46 ft. long and 14 ft. 9 in. wide, with matting 14 yd. wide, at $.25 a yard. It will require 4 strips of matting, each 15 yd. long.

14. How many yards of velvet carpeting, 14 yd. wide, will cover a parlor floor 24 ft. long and 17 ft. wide, if the strips run lengthwise, and 9 in. to be turned under at

atching of the figures requires end of the room?

15. How many yards of Brussels carpeting, yd. wide, will cover the same floor, and what will be its cost, at $1.65 a yard, if the strips run lengthwise, and the matching of the figures requires 6 in. to be turned under?

16. How many squares are there in a partition 104 ft. 9 in. long, and 20 ft. 4 in. high?

17. Find the cost of plastering the sides and ceiling of a room 40 ft. long, 36 ft. wide, and 221 ft. high, at $.36 a sq. yd., allowing 1375 sq. ft. for doors, windows, and baseboard.

18. How many planks 16 ft. long and 9 in. wide, will be required to floor a room 36 ft. long and 24 ft. wide?

19. Find the cost of glazing 6 windows, each 8 ft. 3 in. by 5 ft. 4 in., at $.75 a square foot.

20. How many sods, each 16 in. square, will be required to turf a yard 53 ft. 4 in. long and 28 ft. wide?

21. How many shingles averaging 4 in. wide, laid 6 in. to the weather, will cover the roof of a building 46 ft. long, each of the two sides being 20 ft. wide from the eaves to the ridge, the first course on each side being double?

22. What will be the cost of wainscoting a room 21 ft. 8 1 by 14 ft. 10 in., and 10 ft. 6 in. high, at $.30 a sq. yd.?

23. Find the cost of slating a roof 64 ft. 9 in. long and 45 ft. wide, at $15.37 per square?

24. What is the area of a square field, the distance around which is 560 rods?

25. Find the cost of painting a roof 52 ft. long and 30 ft. wide, at $.75 a square.

SOLIDS.

219. A solid has three dimensions, length, breadth, and thickness or height.

220. A rectangular solid is a body

bounded by six rectangu

lar faces.

Rectangular Solid.

Cube.

A cube is a rectangular body whose faces are all equal.
The opposite sides are equal and parallel.

221. The unit of measure for solids is a cube, the edge of which is a unit of some known length.

Thus, the unit of cubic inches is a cube, the edge of which is 1 inch, or 1 cubic inch; of cubic feet, 1 cubic foot, etc.

222. The volume or solid contents of a rectangular body is the space included within the surfaces which bound it, and is expressed by the product of the numbers representing its three dimensions, or by the number of times it contains a given unit of measure.

which are 27 cu. ft. Hence the volume of 1 cu. yd. is 27 cu. ft.

So the volume of a solid, formed of two adjacent sections, is expressed by 3 cu. ft. x 3×2 = 18 cu. ft.

223.

FORMULAS FOR RECTANGULAR SOLIDS.

1. Length x breadth x height = volume.
2. Volume (length x breadth) = height.
3. Volume (length x height) = breadth.
4. Volume (breadth x height) = length.

The three given dimensions must be expressed in units of the same denomination.

For measures of volume, the following units are used:

The cubic foot for bricklaying, masonry, and hewn timber.

The cubic yard for embankments, excavations, and masonry.
A cubic yard of common earth is sometimes called a load.

The perch of stone, 16 ft. long, 1 ft. wide, and 1 ft. high, equal to 24 cu. ft. It is customary, however, to call 25 cu. ft. a perch.

Brick.-The size of a common brick is 8 x 4 x 2 in., and for ordinary calculation it is sufficiently accurate to reckon 27 bricks to the cubic foot, laid dry, or 22 laid in mortar.

Brickwork is generally estimated by the thousand bricks. In estimating material, allowance is made for openings in walls, as doors, windows, etc.

In estimating labor, the length of each wall is measured on the outside, and thus each corner is measured twice.

Sometimes, by special contract, an allowance is made for one half the openings and corners.

224. 1. What is the volume of a rectangular solid 22 ft. long, 13 ft. wide, and 5 ft. thick?

SOLUTION.—22 × 13 × 5 = 1430; hence, the volume is 1430 cu. ft. (223, 1).

2. A tank 14 ft. long and 12 ft. wide contains 1566 cu. ft. What is its depth?

SOLUTION.-1566÷141 × 12 = 9; hence, the depth is 9 ft. (223, 2.) 3. In a solid 3 ft. 2 in. long, 2 ft. 2 in. wide, and 1 ft. 8 in. thick, how many cubic inches?

4. A vat 12 ft. square contains 1224 cu. ft. What is its depth?

5. What is the volume of a bin, the inside dimensions of which are 8 ft. 6 in. by 6 ft. by 4 ft. 4 in.?

6. How many cubic yards of earth must be removed in digging a cellar 36 ft. long, 24 ft. wide, and 6 ft. deep?

Find the volume of rectangular solids having the following dimensions:

7. Of a cube the edge of which is 1 yd. 1 ft. 9 in.

8. Of a solid 6 yd. 2 ft. 7 in. by 3 ft. 4 in. by 2 ft. 11 in. 9. Of a solid 5 ft. square and the height 6.4 ft.

10. My sleeping room is 10 ft. long, 9 ft. wide, and 8 ft. high. If I breathe 10 cu. ft. of air in one minute, in how long a time will I breathe as much air as the room contains?

11. How many cords in a pile of wood 30 ft. long, 8 ft wide, and 6 ft. 6 in. high?

12. A pile of wood containing 67 cords, is 90 ft. long and 12 ft. wide. How high is it?

15. How much wood is there in a pile 8 ft. long, 6 ft. wide, and 5 ft. 4 in. high?

16. How many perches of masonry in a wall 120 ft. long, 6 ft. 9 in. high, and 18 in. thick?

17. At $3 a cord, what is the value of the wood that can be piled under a shed 50 ft. long, 25 ft. wide, and 12 ft. high? 18. A cellar wall, 32 ft. by 24 ft., is 6 ft. high and 11⁄2 ft. thick. What did it cost, at $1.25 a perch?

19. What must be the length of a load of wood that is 3 ft. high and 5 ft. 4 in. wide, to contain a cord?

20. At $.56 a cu. yd., what will it cost to remove an embankment 240 ft. long, 38 ft. wide, and 8.5 ft. high?

21. What will it cost to build a wall 240 feet long, 6 feet high, and 3 ft. thick, at $3.25 per 1000 bricks, each brick being 8 in. long, 4 in. wide, and 2 in. thick ?

22. How many cans, 6 in. by 4 in. by 3 in. can be packed in a box 24 in. by 18 in. square, in the clear?

23. Find the cost of digging and walling the cellar of a house, whose length is 41 ft. 3 in., and width 33 ft.; the cellar to be 8 ft. deep, and the wall 14 ft. thick. The excavating will cost $.50 a cu. yd., and the stone and mason work $3.75 a perch.

24. In a school-room 32 ft. long, 18 ft. wide, and 12 feet high, are 60 pupils, each breathing 10 cu. ft. of air in a minute. In what time will they breathe as much air as the room contains?

25. How many perches of stone will be required to enclose a lot 16 rd. long and 12 rd. wide, with a wall 6 ft. high and 3 ft. thick ?

26. A street 650 ft. long and 72 ft. wide, averages 4.5 feet below grade. Find the cost of filling it in, at $.42 a cu. yd. ? 27. How many cubic feet of masonry in the wall of a cellar 37 ft. long, 26 ft. wide, and 9 ft. deep, the wall being 2 ft. thick; and what will be the cost, at $3.85 a perch?