PAINTING, PAPERING, PLASTERING, ETC. 143. Painting, papering, plastering, etc. are estimated by the square foot or square yard. Roofing is generally estimated by the square, which consists of 100 square feet. Shingles are estimated by the thousand. With shingles that average 4 inches in width and are laid 6 in. to the weather, 600 shingles cover a square. 1. What will it cost to paint a house 40 feet long, 30 feet wide, and 20 feet high, at 15 cents a square yard, no allowance being made for doors or windows? 2. What will it cost to plaster 6 rooms, each 20 ft. long, 15 ft. wide, and 10 ft. high, at 40 cents a square yard? 3. What will it cost to slate a roof 40 ft. 6 in. long, each side being 24 ft. wide, at $16 a square? 4. A roof is covered with shingles put 8 in. to the weather; what is the cost at $12 a thousand if the roof is 80 ft. long and each side is 30 ft. wide? · 5. What will it cost to paint a barn 30 ft. long and 20 ft. wide, 16 ft. to the eaves, the gables being 8 ft. high, at 40 cents a square, if it requires 10 gallons of paint at $1.60 a gallon? 6. What will it cost to cover a room 24 feet long and 18 feet wide with carpet 27 in. wide at $1.25 a yard, allowing 5 yards for matching; the strips to be laid lengthwise? 7. What will it cost to cover a hall 33 feet long and 5 feet wide with matting 30 inches wide at 55 cents a yard? 8. What will it cost to cover the roof of a barn 80 feet long and 56 feet wide with shingles which average 4 inches in width and are put 8 inches to the weather, the length of the rafters being of the width of the barn, and the shingles costing $12 per thousand? 9. What will it cost to cover a floor 18 ft. long and 12 ft. 3 in. wide with oil-cloth at 50 cents a square yard? 10. Which will be the cheaper, and how much, to cover a floor 25 feet long and 22 ft. 8 in. wide with matting in strips 2 ft. 10 in. wide, laid lengthwise, at 45 cents a yard, or to cover it with oil-cloth at 50 cents a square yard? 11. What will it cost to plaster a room 18 ft. long, 12 ft. wide, and 10 ft. high, at 41 cents a square yard, allowing 90 sq. ft. for doors and windows? 12. How many rolls of paper, each containing 36 sq. ft., will be required to paper a room 16 ft. long, 15 ft. wide, and 10 ft. high, no allowance being made for doors and windows? 13. What will the paper cost for a room 20 ft. long, 16 ft. wide, and 12 ft. high, with paper 18 in. wide and 8 yd. long, at 20 cents a roll, allowing 100 sq. ft. for doors and windows? 14. What will it cost to paper a room 21 ft. long, 15 ft. wide, and 10 ft. high, with paper 18 in. wide and 8 yd. long, at 24 cents a roll, allowing for 3 windows 6 ft. by 3 ft., and 4 doors 7 ft. by 34 ft., if the work can be done by 2 men in 1 day at $2.50 each per day? 15. A frame barn is covered with shingles put 6 in. to the weather; what is the cost at $11 a thousand if the roof is 60 ft. long, each side being 32 ft., the first course along the eaves being doubled? 16. How many yards of plain matting 30 inches wide will be required to cover a hall 65 feet long and 30 feet wide, there being no allowance for waste and the strips running lengthwise? How many yards if the strips run crosswise? MEASURES OF VOLUME. 144. A Volume is that which has length, breadth, and thickness. A volume is called a solid. THE RECTANGULAR SOLID. A Rectangular solid is a volume bounded by six rectangular faces. A Cube is a volume bounded by six equal squares. 9 The Contents of a volume is the number of cubic units it contains. Thus, in the volume ABCDEF the contents is the number of small cubes it contains, which is equal to the number in the base A multiplied by the number of layers; hence the whole number of cubes, or the con B D tents, equals the product of the length, breadth, and thickness. Hence the RULE. To find the contents of a rectangular volume, take the product of the length, breadth, and height. WRITTEN EXERCISES. 1. How many cubic feet in a rectangular block 8 ft. long, 6 ft. wide, and 4 ft. high? 2. How many cubic yards of earth in a cellar 36 ft. long, 24 ft. wide, and 5 ft. deep? 3. Find the contents of a cube 8 ft. 6 in. on a side. 4. How many cubic feet of water in a rectangular reservoir 80 ft. long, 60 ft. wide, and 10 ft. deep? What is its weight, if a cubic foot of water weighs 62 lbs.? 5. How many cords in a pile of wood 72 ft. long, 12 ft. wide, and 8 ft. high? 6. What is the cost of a pile of wood 120 ft. long, 8 ft. wide, and 10 ft. high, at $5.25 per cord? 7. What will be the cost of the bark that can be piled in a shed 120 ft. long, 60 ft. wide, and 15 ft. high, at $6 a cord? 8. What will it cost to dig a cellar for a house 40 ft. long, 32 ft. wide, and 4 ft. 6 in. deep, at $1.50 a cubic yard? 145. A Cylinder is a round body with equal parallel circles for its bases, and having a uniform diameter. The Altitude of a cylinder is the perpendicular distance between its bases. The Convex Surface of a cylinder is the curved surface which bounds it. If the convex surface of a cylinder be unfolded, it will form a rectangle whose length is the circumference of the base, and whose altitude is the height of the cylinder. Hence the RULE. To find the convex surface of a cylinder, multiply the circum ference of the base by the altitude. To find the contents of a cylinder: RULE. To find the contents of a cylinder, multiply the area of the base by the altitude. WRITTEN EXERCISES. 1. Find the convex surface of a cylinder whose altitude is 12 ft. and the radius of the, base 5 ft. 2. How many cubic feet in a cistern 8 ft. deep and 6 ft. in diameter? 3. What is the convex surface of a cylinder whose altitude is 20 ft. and the diameter of the base 20 ft.? 4. Find the convex surface and the contents of a cylinder 5 ft. in diameter and 30 ft. high. 5. How many cubic feet in a log 24 ft. long and 4 ft. in circumference? 6. A bushel measure is a cylinder 18 in. in diameter and 8 in. deep; find the contents. 7. What will it cost to paint the outside of a stand-pipe 75 ft. high and 10 ft. in diameter at 10 cents a square yard? 8. How many cubic feet of iron in a tube 30 ft. long whose circumference is 37.6992 inches, the thickness of the material being 2 inches? 9. Which is the larger, and how much, a cylinder whose circumference is 12 feet, or a volume whose base is a square 12 ft. in perimeter, both being 10 ft. high? 10. The volume of a cylinder is 2513.28 cu. ft., and the diameter of the base is 20 ft.; what is the altitude, and what is the convex surface? |