RECTANGULAR SOLIDS.

469. A Rectangular Solid is a body bounded by six rectangular plane faces.

The opposite sides are equal and

parallel.

It has three dimensions-length, breadth, and thickness.

When all its faces are equal, it is called a Cube.

470. The Volume or Solid Contents of a body is the space included within the surfaces which bound it, and is expressed by the number of times it contains a given unit of measure.

471. 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.

contains 3 such sections, or 3 times 9 cu. ft., 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 ex pressed by 3 cu. ft. x 3 x 2 = 18 cu. ft.

472. To find the volume of a rectangular solid

RULE. Find the product of the numbers denoting the three dimensions, expressed in the same denomination; this result is the volume.

473. To find a required dimension of a rectangular solid:

RULE.-Divide the volume by the product of the numbers denoting the other two dimensions; the quotient will be the required dimension.

474. 1. What are the contents of a rectangular solid 6 ft. long and 4 ft. square?

2. What is the volume of a solid 9 ft. long, 4 ft. wide, and 3 ft. thick ?

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

4. 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.?

5. 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:

6. Of a cnbe the edge of which is 1 yd. 1 ft. 9 in.

7. Of a solid 6 yd. 2 ft. 7 in. by 3 ft. 4 in. by 2 ft. 11 in. 8. Of a solid 5 ft. square and the height 6.4 ft. Find the required dimension of rectangular solids, the volumes and two dimensions being as follows:

9. Volume, 6 cu. ft.; length, 8 ft.; width, 8 ft. 10. Volume, 20 cu. ft.; length, 36 ft.; width, 10 in.

11. Volume, 13 cu. yd. 14 cu. ft. 900 cu. in.; width, 7 ft. 3 in.; height, 5 ft. 6 in.

12. How many cubic feet of air in a room that is 24 ft. 9 in. long, 18 ft. 4 in. wide, and 10 ft. 8 in. high?

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

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

15. What will be the cost of a pile of wood 12 ft. 6 in. long, 8 ft. wide, and 4 ft. 6 in. high, at $3.75 a cord?

16. What will it cost to dig a cellar 45 ft. long, 28 ft. wide, and 8 ft. 6 in. deep, at $.42 a cubic yard?

17. 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?

18. How many cans, 8 in. by 6 in. by 3 in., can be packed in a box 32 in. by 24 in. by 15 in. in the clear?

19. 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?

20. In building a house, 200 joists 10 in. by 3 in. were used, which together amounted to 1000 cu. ft. What was the length of each?

475. Masonry is estimated by the cubic foot, and by the perch; also by the square foot and the square yard.

1. Materials are usually estimated by cubic measure; the work by cubic or square measure.

2. A Perch of stone, or of masonry, is 161 ft. long, 1 ft. wide, and 1 ft. high, and is equal to 24.75 cu. ft.

3. When stone is built into a wall, 22 cu. ft. make a perch, 2 cu. ft being allowed for mortar and filling.

4. Embankments and Excavations are estimated by the cubic yard. 5. A cubic yard of common earth is called a load.

6. Brickwork is generally estimated by the thousand bricks; sometimes in cubic feet. In walls, brick-work is estimated at the rate of a brick and a half thick.

7. North River bricks are 8 in. × 3 × 2; Maine bricks are 7 in. ×3×2; Philadelphia and Baltimore bricks are 8 in. × 4 × 2 ; and Milwaukee bricks 8 in. × 43 × 28.

8. In estimating material, allowance is made for doors, windows, and cornices.

9. In estimating the work, masons measure each wall on the outside, and ordinarily, no allowance is made for doors, windows, and corners; but sometimes an allowance of one-half is made, this being, however, a matter of contract.

476. To find the number of bricks in a cubic foot of masonry:

RULE.-I. Add to the face dimensions of the kind of bricks used the thickness of the mortar or cement in which they are laid, and compute the area.

II. Multiply this area by the quotient of the thickness of the wall divided by the nnmber of bricks of which it is composed, the product will be the volume of a brick and its mortar in cubic inches.

III. Divide 1728 by this volume, and the quotient will be the number of bricks in a cubic foot.

477. 1. of wall 12 thick ?

How many Milwaukee bricks in a cubic foor in. wide, laid in courses of mortar of an inch

OPERATION.

8.5+.25 8.75 in. = length of brick and joint.

2.375+.252.625 in. thickness of brick and joint.

=

8.75 x 2.625 = 22.96875 sq. in. area of its face.

12.753 (number of bricks in width of wall) = 4.25 in. width of brick and mortar.

22.96875 x 4.25 97.617+ = cubic inches in a brick.

=

172897.617+ = 17.7+ = number of bricks in a cubic foot.

2. How many bricks, 8 in. x 4 x 2, will be required to build a wall 42 ft. long, 24 ft. high, and 164 in. thick, laid in courses of mortar of an inch thick?

3. How many perches of stone, laid dry, will build a wall 60 ft. long, 161 ft. high, and 18 in. thick?

RULES.-1. Multiply the number of cubic feet in the wall, or work to be done, by the number of bricks in a cubic foot; the product will be the number of bricks required.

2. Divide the number of cubic feet in the work to be done by 24.75; the quotient will be the number of perches.

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

5. How many bricks in the four walls of a square house 36 ft. long, 24 ft. high, and 12 in. thick, allowing 224 cu. ft. for doors and windows, one half for the corners, and of an inch for each course of mortar?

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