Page images
PDF
EPUB
[blocks in formation]

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÷14 × 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?

13. 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?

14. 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?

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 14 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 1 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, allowing one-half for corners?

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 cu. ft. in the wall of a cellar 371 ft. long, 26 ft. wide, and 9 ft. deep, the wall being 2 ft. thick, allowing onehalf for corners; and what will be the cost, at $3.85 a perch?

BOARDS AND TIMBER.

225. A board foot is 1 ft. long, 1 ft. wide, and 1 inch thick. Hence, 12 board feet make 1 cubic foot.

Board feet are changed to cu. ft. by dividing by 12, and cubic feet are changed to board feet by multiplying by 12.

1. In board measure, all boards are assumed to be 1 in. thick; if less than 1 in., the difference is disregarded; if more than 1 in., the quantity is increased one fourth for every additional in. in thickness. Thus,

1200 sq. ft., 1 in. thick or less = 1200 ft. board measure.

[merged small][merged small][merged small][merged small][merged small][ocr errors][ocr errors]

2. Lumber and sawed timber such as plank, scantling. joists, etc., are usually estimated in board measure.

3. Hewn and round timber are commonly estimated in cubic measure.

[blocks in formation]

226. To find the contents of a piece of lumber.

1. Find the contents of a board 15 ft. long and 8 in. wide. SOLUTION.-15 x 8÷12 = 10 board feet.

2. What are the contents in board measure of a joist 16 ft. long, 10 in. wide, and 3 in. thick ?

SOLUTION.-3 × 10 × 16÷12 = 40 board feet. Hence,

RULE.-Multiply the length in feet by the width and thickness in inches, and divide the product by 12 for board feet, or by 144 for cubic feet.

1. If one of the dimensions is inches, and the other two are feet, the product will be board feet.

2. If a board tapers regularly, multiply the length by the mean width, found by taking half the sum of the two ends.

[blocks in formation]

12. Find the contents of a board 18 ft. long, 1 ft. 8 in. wide at one end, and 14 in. at the other.

SOLUTION.-20 in. + 14 in.÷2 = 17 in.; 18 x 17÷12

=

251 board ft.

13. Find the cost of 5 boards 12 ft. long, 17 in. wide at one end and 11 in. at the other, at 6 cents a square foot.

14. Find the cost of 10 planks, each 15 ft. long, 16 in. wide, and 34 in. thick, at $2.25 per hundred feet.

15. Find the cost of 3 pieces of timber, each 26 ft. long and 6 in. by 9 in., at $1.75 per hundred board feet.

16. Find the cost of 8 pieces of scantling, 3 in. by 4 in. and 14 ft. long, at $9.50 per thousand board feet.

17. What amount of inch lumber will make a box 4 ft. by 3 ft. 6 in. by 2 ft. 6 in. on the outside.

Find the cost of the following:

18. Of 36 boards, 12 ft. long, 11 in. wide, @ $2 per C. 19. Of 16 planks, 14 ft. long, 10 in. wide, and 3 in. thick, @ $161 per M.

20. How many board feet in a stick of timber 36 ft. long, 10 in. thick, 12 in. wide at one end and 9 in. wide at the other end? How many cubic feet?

21. How much flooring 11⁄2 in. thick will be required to lay the floors of a two-story house, 48 ft. by 38 ft., no allowance being made for waste; and what will be its cost, at $35 per M.?

22. A field 64 rd. by 32 rd. is enclosed by a board fence; the posts are set 8 ft. apart, the boards are 16 ft. long, and the fence is 5 boards high. The bottom board is 12 in., the top board 6 in., and the others each 9 in. wide. The posts cost $25 per C., and the boards $14.80 per M. Find the number of posts, the amount of lumber, and the cost of both.

RECTANGULAR BINS, CISTERNS, ETC.

227. Cubic measures are used to ascertain the capacity of rectangular cisterns, bins, etc., but the results are generally expressed in units of liquid and dry measures.

228. COMPARATIVE TABLE OF MEASURES OF CAPACITY.

[blocks in formation]

A cubic foot of pure water weighs 1000 oz., equals 621⁄2 lb. Avoir.
The standard bushel of the United States contains 2150.42 cu. in.

The stricken or even bushel is the unit of measure for grain, seeds, and small fruits.

The heaped bushel is the unit of measure for coal, lime, corn in the ear, large fruits, root crops, etc., and contains 2747 7 cu. in. Hence,

A cubic foot may be considered .8 of a bushel STRICKEN measure, or .63 of a bushel HEAPED measure.

[blocks in formation]

229. To find the exact capacity of a vessel or space in gallons.

1. How many gallons of water will a cistern hold, that is 4 ft. square and 6 ft. 9 in. deep?

=

SOLUTION.-(4 × 4 × 6 × 1728)÷231 80799 gal.

2. How many cubic feet in a space that holds 48 hhd. ? SOLUTION.-(48 × 63 × 231)÷÷1728

=

4041 cu ft.

RULE.-Divide the contents in cubic inches by 231 for LIQUID gallons, or by 268.8 for DRY gallons.

Conversely, to reduce gallons to cubic inches:

Multiply the given number of liquid gallons by 231; then reduce to higher denominations, if required.

« PreviousContinue »