SUPPLEMENTARY PROBLEMS. To be omitted unless otherwise directed 6. What will it cost to shingle a roof 64 ft. long and 82 feet from eaves to ridge, the first course along the eaves being double, at $14.87} a thousand ? Ans. $614.992. 7. What will it cost to paper a room 40 ft. long, 32 ft. 4 in. wide, and 154 ft. high, allowing 815 sq. ft. for doors, windows and wasbboards, at 25per sq. ft.; ceiling not included ? Ans. $356.83]. 8. A cistern 7 ft. 5 in. long, 4 ft. 6 in. wide, and 6 ft. 3 in. deep, is to be lined with zino costing 129 a pound, allowing 5 lb. to the square foot; what will be the expense ? Ans. $109.40. CARPETING AND PAPERING. 348. In Carpeting we take into consideration the width of the carpet, the allowance for matching the figures, and whether the strips run lengthwise or crosswise. To match the figures we must often turn under or cut off one of the ends. When an exact number of strips is a little too wide for the room, one breadth is turned under. Rule.-Find the number of strips required, and multiply the number of yards in each strip by the number of strips. WRITTEN EXERCISES 1. How many yards of carpet, 1 yd. wide, will be required to carpet a floor 18 ft. 8 in. by 14 ft. 9 in., running lengthwise. SOLUTION.—The room is nearly 5 yd. wide, hence it will require 5 strips, or breadths, each 189 ft. long; and it will take 183 ft. X5= 93} ft., or 31+ yds. 2. A lady wishes to cover her sitting-room, 31 ft. long and 15 ft. wide, with matting 24 ft. wide, no allowance required for matching; how many yards will it take, running lengthwise ? How many running crosswise ? Ans. 62 yds. ; 65 yds. 3. How many yards of Brussels carpet, 1 yd. wide, will it take to carpet a parlor 26 ft. long by 15 ft. wide, the strips running lengthwise, the matching of figures requiring 6 in. to be cut off each strip except the first? Ans. 611 yds. ing? 4. Miss Hartman wishes to caipet (lengthwise) a room 18 ft. long by 14 ft. 6 in. wide, with Brussels carpet of a yard wide, at $1.25 a yard; what will it cost, 2 yarıls waste for match Ans. $62.50. SUPPLEMENTARY PROBLEMS, To be omitted unless otherwise directed. 5. How many rolls of paper 8 yds. long and 20 in. wide, will cover the walls and ceiling of a room 30 ft. long, 224 ft. wide and 10 ft. 8 in, high, deducting 142 sq. ft. for openings ? Ans. 4178 rolls. 8. What will be the cost of papering the above room at $2.40 a roll, putting also a gilt moulding around the top of the walls, at 12 cents a foot? Ans. $111.78. 7. A room contained 3 windows, which were curtained with bro catelle of a yard wide; 10 yards were required for each window @ $1.50, and the curtains were lined with silk of a yard wide @ $.87}; how many yards of silk were required, and what was the whole cost of the curtains ? Ans. 24 yd.; $66. MEASURES OF VOLUME. 349. A Volume is that which has length, breadth, and thickness or height. These three elements are called dimen. sions. A volume is also called a solid. 350. A Rectangular Volume or Solid is a volume bounded by six rectangles. The bounding rectangles are called faces. Cellars, boxes, rooms, etc., are examples of rectangular volumes. 3 feet wide. 351. A Cube is a volume bounded by six equal squares. Or, a cube is a rectangular volume whose faces are all equal. 352. By the Contents or Solidity of a volume we mead the amount of space it contains. The contents are expressed by the number of times it contains a cube as a unit of meas. 3 feet high. ure. Rule I.- To find the contents of a cube or rectangular volume, take the product of its length, breadth, and height. For, in the volume above, the number of cubic units on the base equals the length multiplied hy the breadth or 3x3= - 9. and the whole number of cubic units equals the number on the base multiplied by the numbes of layers of these cubes, or 9X3=27; hence the whole number of cubes, or the qfntents, equals the product of the length, breadth, and height. Rule 11.– To find either dimension, divide the contents by the product of the other two dimensions. WRITTEN EXERCISES. 1. What are the contents of a room 18 ft. long, 14 ft. wide nd 10 ft. high? SOLUTION.—To find the contenus, we multiply the length, breadth, and height together, and we have 18x14x10=2520 cu. ft.; reducing this to cubic yards, we have 93 cu. yd. 9 cu. ft. 2. What are the solid contents of a cube whose edge meas ures 1 yd. 1 ft.? Ans. 2 cu. yd. 10 cu. ft. 3, A cistern 9 ft. square contains 405 cubic feet ; wbat is its depth ? Ans. 5 ft. 4. How many cubic inches in a rectangular block of marble 6 ft. long, 4 ft. wide, and 2 ft. thick? Ans. 103680. 5. How many cubic yards of air in a room 25 ft. long, 12 ft 6 in. wide, and 9 ft. high? Ans. 10918 cu. yd. 6. A pile of bricks contains 125 cubic yards, and is 13 ft. 6 in. wide, and 8 ft. 4 in. bigb; what is its length ? Ans. 30 ft. 7. How much earth will be dug out of a cellar 72 ft. long, 48 ft. wide, and 7 ft. 3 in. deep? Ans. 928 cu. yd. THE CYLINDER. 353. A Cylinder is a round body of uniform size, with equal and parallel circles for its onds. The two circular ends are called bases. 354. The Altitude of a cylinder is the distance from the centre of one base to the centre f the other. 355. The Convex Surface of a cylinder is the sorface of the curved part. Rule I.— To find the convex surface of a cylinder, mul tiply the circumference of the base by the altitude. Rule II.- To find the contents of a cylinder, multiply the area of the base by the altitude. WRITTEN EXERCISES. 1. What is the convex surface of a cylinder, the diameter oi whose base is 8 inches and whose altitude is 12 incbes ? SOLUTION.—The circumference of the base equals 8X 3.1416, which is 25.1328 inches ; multiplying by the altitude, 12, we uave 301.5936 square inches, the convex surface. 2. I have a log 18 ft. long and 20 inches in diameter; how many square feet of bark on the log ? Ans. 94.248 sq. ft. 3. A well is 10 feet deep, and 3 feet in diameter ; how many cubic feet does it contain ? Ans. 70.686 cu. ft. 4. What is the cost of digging a well 15 ft. deep and 9 ft. in circumference, at $.627 a cubic yard? Ans. $2.24—. 6. How much zinc will it take to line the sides of a cisterp 8 ft. in diameter and 81 feet deep ? Ans. 23.0384 sq. yd. 6. Dr. Hiestand put in his house a cistern, 10 ft. in diame. ter and 4 ft. 6 in. bigb; how many cubic feet of water did it hold? Ans. 353.43 cu. ft. WOOD MEASURE. 356. The Measure of Wood is the cord, which is divided into cord feet, etc. 357. A Cord of wood is a pile 8 feet long, 4 feet wide, and 4 feet high. It contains 8 cord feet, or 128 cubic feet. 358. A Cord Foot is a part of this pile 1 foot long. It is thus 1 foot long, 4 feet wide, and 4 feet high, and contains 16 cubic feet. Rule.- To find the number of cords in a pile of wood. find the number of cubic feet and reduce to cord feet ano cords. WRITTEN EXERCISES. 1. How many cords in a pile of wood 28 ft. long, 10 ft. high, and 10 ft. wide ? SOLUTION.—The number of cubic feet equals 28X10X 10, which equals 2800 ; dividing by 16, to reduce this to cord feet, we have 176 ord feet; dividing by 8 to reduce this to cords, we have 21 cd. 7 od ft. 2. How many cords in a pile of wood 96 ft. long, 12 ft wide, and 8 ft. bigb? Ans. 72 cords. 3. A load of wood containing exactly 1 cord, is 5 ft. 4 in. wide, and 3 ft. 9 in. high ; what is its length? Ans. 6% ft. 4. What is the height of a pile of wood containing 273 cords, if it is 75 ft. long and 10 ft. wide ? Ans. 4.736 ft. 5. What will be the cost of the wood that can be piled in a shed 20 ft. long, 10 ft. wide, and 8 ft. high, at $4.75 a cord? Ans. $59.374 BOARDS AND TIMBER. 359. Boards and Timber are usually estimated in what are called board feet, instead of in cubic feet. 360. A Board Foot is 1 foot long, 1 foot wide, and 1 inch thick. A cubic foot, therefore, contains 12 board feet. Hence, board feet may be reduced to cubic feet by dividing by 12, and cubic feet to board feet by multiplying by 12. A standard board, in commerce, is 1 inch thick, and its contents in board feet are the product of its length and breadth in feet. Board feet are usually known as square feet. Boards are quoted by the hundred or the thousand, meaning a hundred square feet, or a thousand square feet. Round timber, as masts, etc., is estimated in cubic feet; hewn timber, as beams, etc., either in board or cubic feet; lumber and sawed timber, as planks, scantling, joists, etc., in board feet. Rule I.-To find the contents of a board, multiply the length in feet by the width in inches, and divide the product by 12. Rule II.- To find the contents of a plank, joist, etc., multiply the length in feet by the width and thickness in inches, and divide the product by 12. Notes.-1. If one of the dimensions is inches and the other two are foet, whe product will be board feet. 2. When a board tapers regularly, the length must be multiplied by the mean width, which is half the sum of the two ends. WRITTEN EXERCIS ES. 1. What are the contents of a board 14 feet long and 9 inches wide ? SOLUTION.-Multiplying the length in feet by the width in inches, we have 14X 9=126; and dividing by 12, we have 104 board feet, or acreare feet. |