6. 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 board foot. 7. Find the cost of 10 planks, each 15 ft. long, 16 in. wide, and 3 in. thick, at $2.25 per hundred feet. 8. What length of board 9 in. wide contains 8 board ft. ? OPERATION. 144 x 8+9=128; 128÷ 12 = 103 ft., the length. 9. What length may be cut from a board 15 ft. long and 20 in. wide, so as to leave 15 board feet? 10. What must be the width of a board 16 ft. long, to contain 12 board feet? OPERATION. 16 ft. 192 in.; 144 × 12 ÷ 1929 in., the width. = 11. What must be the width of a piece of board 5 ft. 3 in. long, to contain 7 square feet? 12. 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. 13. Find the cost of 8 pieces of scantling, 3 in. by 4 in. and 14 ft. long, at $9.50 per thousand board feet. 14. What length of a piece of timber 6 in. by 9 in., will contain 3 cubic feet? OPERATION. 1728 x 39 x 696; 96+128 ft., the length. 15. A piece of timber is 10 in. by 16 in. What length of it will contain 15 cubic feet? 16. What amount of inch lumber will make a box 4 ft. by 3 ft. 6 in. by 2 ft. 6 in. on the outside? 17. Find the cost of 36 boards, 12 ft. long, 11 in. wide, @$2 per C. 18. Find the cost of 16 planks, 14 ft. long, 10 in. wide, and 3 in. thick, @ $161 per M. CAPACITY OF BINS, CISTERNS, ETC. 230g. The Standard Bushel of the United States contains 2150.42 cubic inches, and is a cylindrical measure 18 inches in diameter and 8 inches deep (203). 1. Measures of capacity are all cubic measures, solidity and capacity being measured by different units, as seen in the tables. 2. Grain is shipped from New York by the quarter of 480 lb. (8 U. S. bu.), or by the ton of 333 U. S. bushels. 3. It is sufficiently accurate in practice to call 5 stricken measures equal to 4 heaped measures. 4. Ordinary anthracite coal measures from 36 to 40 cu. ft. to the ton; bituminous coal, from 36 to 45 cu. ft. to the ton. 5. Lehigh, white ash, egg size, measures about 34 cu. ft. to the ton (2000 lb.); Schuylkill, white ash, 35 cu. ft.; and of gray or red ash, 36 cu. ft. to the ton. 6. Coal is bought and sold in large quantities by the ton; in small quantities by the bushel, the conventional rate being 28 bu. (5 pecks) to a ton, or about 43.5 cu. ft. EXAMPLES. 230h. To find the exact capacity of a bin in bushels. RULE. -I. Divide the contents in cubic inches by 2150.42; the quotient will represent the number of bushels. Since a standard bushel contains 2150.42 cu. in., and a cubic foot contains 1728 cu. in., a bushel is to a cubic foot nearly as 4 to 5; or a bushel is equal to 14 cu. ft., nearly. Hence for all practical purposes, II. Any number of cubic feet diminished by will represent an equivalent number of bushels. Thus, 250 cu. ft. of 250 cu. ft., or 50 cu. ft. = 200, the number of bushels in 250 cu. ft. III. Any number of bushels increased by will represent an equivalent number of cubic feet. Thus, 200 bu. + of 200 bu. or 50 bu. = 250, the number of cubic feet in 200 bushels. PRAC. AR.-15 1. How many bushels of wheat can be put in a bin 8 ft. long, 6 ft. 6 in. wide, and 3 ft. 4 in. deep? 2. What must be the depth of a bin to contain 240 bu., its length being 10 feet and its width 5 feet? OPERATION. 240+60 300. 300 ÷ 10 × 5 = 6; 6 ft., the depth. RULE. Divide the contents in cubic feet or inches by the product of the two dimensions, in the same denomination. 3. What must be the length of a bin that is 6 feet wide and 4 feet deep, to contain 324 bushels? Ans. 15 ft. 4. How many bushels of apples will a bin hold, that is 12 ft. long, 3 ft. wide, and 2 ft. 6 in. deep? How many of barley? 5. A bin 20 ft. long, 12 ft. wide, and 5 ft. deep, is full of wheat. What is its value at $2 a bushel? 6. A bin full of rye. 7 ft. long, 6 ft. wide, and 5 ft. deep, is What is its value at $1.371⁄2 a bushel ? 7. A crib, the inside dimensions of which are 15 ft. long, 7 ft. 4 in. wide, and 8 ft. high, is full of corn in the ear. If 2 bushels of ears make 1 bushel of shelled corn, what is the value of the whole, when shelled, at $.92 a bushel? Ans. $323.84. 8. If 1 bu. or 60 lb. of wheat make 48 lb. of flour, how many barrels of flour can be made from the contents of a bin 10 ft. long, 5 ft. wide, and 4 ft. deep, filled with wheat? Ans. 39 bbl. 9. How many tons of red ash coal, egg size, will a bin 17 ft. long, 6 ft. wide, and 3 ft. deep contain? 10. A bin 6 ft. long, 4 ft. deep, and 5 ft. 9 in. wide is full of Lehigh white ash coal. Find its value at $6.75 a ton. 11. Find its value if full of Schuylkill white ash, at $5.90 a ton. If full of Schuylkill red ash, at $5.50 a ton. 230i. 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 feet square and 6 feet deep? OPERATION. (4 × 4 × 6 × 1728) ÷ 231 = 7181 gal., capacity. RULE. – Divide the contents in cubic inches by 231 for liquid gallons, or by 268.8 for dry gallons. 2. How many cubic feet are there in a space that holds 48 hhd.? 3. How many hogsheads will a cistern 11 ft. long, 6 ft. wide, and 7 ft. deep contain? Ans. 54% hhd. 4. How many gallons will a space contain that is 22.5 ft. long, 3.25 ft. wide, and 6.4 ft. deep? 5. A man constructed a cistern to hold 32 hogsheads, the bottom being 6 ft. by 8 ft. What was its depth? house is 6 ft. 6 in. long, How many gallons of 6. A tank in the attic of a 4 ft. wide, and 3 ft. 6 in. deep. water will it hold? 7. If 64 quarts of water are put into a vessel that will exactly hold 64 quarts of wheat, how much will the vessel lack of being full? Ans. 604.8 cu. in. 8. If a man buys 10 bu. of chestnuts at $5 a bushel, dry measure, and sells the same at 25 cents a quart, liquid measure, how much does he gain? Ans. $43.09. 9. A cistern 5 ft. by 4 ft. by 3 ft. is full of water. If it is emptied by a pipe in 1 h. 30 min., how many gallons are discharged through the pipe in a minute? 10. A vat that will hold 5000 gallons of water, will hold how many bushels of corn? Ans. 537 bu. 11. A cellar 40 ft. long, 20 ft. wide, and 8 ft. deep is half full of water. What will be the cost of pumping it out, at 6 cents a hogshead? Ans. $22.80. PLASTERING, PAINTING, KALSOMINING. 230j. Plastering, painting, and kalsomining are generally computed by the square yard. The processes of calculating the cost of plastering, painting,,and kalsomining vary so much in different localities that it is impossible to lay down any rule. Usually some allowance is made for doors, windows, etc., on which no work is done; but sometimes the measurements of walls are taken regardless of such openings. At other times, one half the area of the openings is deducted. EXAMPLES. 1. What would it cost to plaster the walls and ceilings of a room 16 ft. long, 15 ft. wide, and 11 ft. high, in which there are 2 doors, 2 ft. 8 in. by 7 ft., and 2 windows, 2 ft. 10 in. by 6 ft. 2 in., at $.37 a sq. yd., deducting half the area for doors and windows? SOLUTION. Two of the walls will be 16 x 11 ft., two, 15 x 11 ft., and the ceiling, 16 x 15 ft. Adding these, we find the total area to be 922 sq. ft. The area of the two doors will be twice 7x2 ft., and of the two windows twice 25 × 6 ft. Adding these, the area of doors and windows is 72.2. We deduct half this area, 36.1, from 922, divide the remainder, 885.9 sq. ft., by 9, to reduce it to square yards, multiply $.37 by the result, 98.4 sq. yd., and find the answer $36.41. 2. What would it cost to plaster the walls and ceiling of a room 12 ft. long, 17 ft. wide, and 10 ft. high, at $.35 a square yard, making no allowance for openings? 3. What will it cost to kalsomine a hall 6 ft. 6 in. × 27 ft. × 11 ft., with 2 coats, at 3¢ a sq. yd. each? 4. What will it cost to paint the walls and ceiling of a room 18 ft. long, 14 ft. wide, 9 ft. high, with 3 coats, at $.07 a sq. yd. each, making no allowance for openings ? |