Written Work 1. Estimate the cost of 378 feet of oak at $26 per M.; of 6389 ft. white pine at $48 per M.; of 972 ft. cherry at $72 per M.; of 693 ft. white ash at $47 per M. wide, and 1 in. thick. wide, and 11⁄2 in. thick. wide, and & in. thick. Find the cost at $35 per M. of: 2. 50 boards, 16 ft. long, 12 in. 3. 60 boards, 12 ft. long, 15 in. 4. 100 boards, 15 ft. long, 6 in. 5. 75 boards, 18 ft. long, 10 in. wide, and 1 in. thick. 6. 45 boards, 16 ft. long, 5 in. wide, and 1 in. thick. Short forms are used by carpenters, architects, and mechanics; thus, one mark (') represents feet, and two marks (") represent inches. Find the number of board feet: 7. 120 studding, 2" × 4′′ × 12'. 23. Estimate the cost of the planks in examples 8 and 18, at $.027 per board foot. 24. Estimate the cost of the sills in examples 12, 14, and 19, at $.032 per board foot. 25. Estimate the cost of the studding in examples 7 and 21, at $.026 per board foot. CONCRETE, STONE, AND BRICKWORK Concrete work is estimated by the cubic yard. Stone work is estimated by the perch, of 24.75 cu. ft., or by the cord of 100 cu. ft. Stones are often sold by the pound. 3200 pounds are estimated to lay 1 perch. In estimating either contract work or cost of labor, in concrete and stone work, the distance around the wall is considered the length. This measures the corners twice. In estimating material, allowance is made for openings and the corners are counted but once. Range work and lintels are measured by the linear foot. Bricks vary Brickwork is estimated by the thousand. in size, but they are usually 8" by 4" by 2". In estimating the number of bricks in a wall, count the corners once, deduct all openings, and multiply the number of square feet remaining in the surface by 7 when the wall is 1 brick thick; by 14 when the wall is 2 bricks thick; and by 21 when the wall is 3 bricks thick. Written Work 1. Find the number of cords of stone in a breakwater 200 ft. long, 14 ft. wide, and 16 ft. high. 2. A building 150 ft. by 130 ft. has a concrete foundation 4 ft. in width and 10 ft. in depth below the structural iron. Estimate the number of cubic yards of material used. 3. If the cement, the gravel, and the sand are in the ratio of 1, 5, and 2, find the number of loads of gravel and of sand used in the construction of the foundation in example 2. 4. Estimate the cost of the concrete work at $7.75 per cubic yard. 5. Estimate the number of cubic yards of concrete in this retaining wall. 6. The walls of a brick house 36 ft. long, 24 ft. wide, and 18 ft. high are 13 in. or 3 bricks thick. Estimate the number of bricks required for the walls, allowing for 11 windows averaging 31 ft. by 6 ft., and 2 doors averaging 31 ft. by 7 ft. 7. A house whose walls are 9 in. or 2 bricks thick is 40 ft. long, 30 ft. wide, and 24 ft. high. Estimate the number of bricks required for the walls, allowing for 12 windows 3 ft. by 7 ft., and 3 doors 31 ft. by 8 ft. 8. The stone work for the foundation of a house 28 ft. by 38 ft. is 1 ft. in thickness and 6 ft. in height to the range work. Estimate the cost of the stone work at $6.30 a perch, and the range work along the two sides and the rear at 60 cents per linear foot. Examine this solid. THE CYLINDER How many ends or bases has it? What is the shape of each? Are the bases equal and parallel? Describe the shape of the body. A cylinder is a solid whose two bases are equal and parallel circles and whose diameter is uniform. HAM. SCH. ARITH.-10 The convex surface of a cylinder is the lateral or curved surface. The altitude is the perpendicular distance between its two bases. Examine this cylinder. Observe: 1. That if a piece of paper is fitted to cover its convex surface and then unrolled, its form will be that of a rectangle. 2. That the circumference of the base is the length of the rectangle, and the altitude of the cylinder is the width of the rectangle. The convex surface of a cylinder is found by multiplying the unit of measure by the product of the circumference and the altitude. The entire surface of a cylinder is found by adding the area of the bases to the convex surface. Written Work Find the convex surface of a cylinder: 1. D. 10 in., height 24 in. 2. D. 15 in., height 30 in. 3. D. 2 ft., height 10 ft. Find the entire surface of: 4. D. 20 in., height 4 ft. 5. D. 8 in., height 4 ft. 6. D. 6 ft., height 15 ft. 7. A water tank 12 ft. in diameter and 12 ft. in height. 8. A steam boiler 15 ft. long and 3 ft. in diameter. Find the volume of a cylinder 3 ft. in diameter and 5 ft. high. 9. Observe: 1. That the area of the base is 32 x .7854 x 1 sq. ft., or 7.0686 sq. ft. 2. That the first row of cubic units contains 7.0686 cu. ft. 3. That the cylinder contains 5 times 7.0686 cu. ft., or 35.343 cu. ft. The volume of a cylinder is found by multiplying the unit of measure by the area of the base and this product by the height of the cylinder. Find the volume of a gas tank, silo, cistern, etc. : BINS, TANKS, AND CISTERNS Wheat and other grains are generally sold by weight, but the capacity of bins is often estimated in bushels. The capacity of tanks and cisterns is estimated in gallons or barrels. NOTE.The, standard bushel in the United States contains 2150.42 cubic inches, stricken measure, and 2747.71 cubic inches heaped measure. 231 cu. in. = 1 gal. 31 gal. = 1 bbl. when estimating contents. Written Work Find contents in bushels of: 1. A bin 20 ft. by 10 ft. by 5 ft. 2. A box 12 ft. x 9 ft. x 6 ft. 3. A metal trough for watering cattle is 12 ft. long, 3 ft. wide, and 20 in. deep. Estimate the number of gallons it holds. 4. A cistern tank for a windmill pump is 8 ft. in diameter and 10 ft. in depth. Estimate the number of barrels of water it holds. 5. The rainfall on a certain day was 11 inches. Find the number of barrels of water that fell on Mr. Anderson's flower plot which is 20 ft. long and 10 ft. wide. |