= 57 2. This figure represents a piece of cement floor at a railroad station. Find its cost at $1.08 a square yard. 3. In this figure, AB = 54 in., CD 18 in., EF = 27 in. Find the area of ACBF in square yards. MEASUREMENT OF RECTANGULAR SOLIDS 227. A solid bounded by six rectangles is E A D F a rectangular solid; e.g. a chalk box. Give other examples. 228. A solid bounded by six squares is a cube. Define cubic inch, cubic foot, and cubic yard. A B 229. The contents or volume of a rectangular solid is the number of cubic units (cu. in., cu. ft., cu. yd.) which it contains, and is equal to the product of its three dimensions. Figure A may represent 5 × 4 × 1 cu. in., cu. ft., or cu. yd. Figure B may represent 5 × 4 × 3 cu. in., cu. ft., or cu. yd. 230. Oral 1. Explain how we determine that there are 27 cu. ft. in 1 cu. yd. 2. Explain how we determine that there are 1728 cu. in. in 1 cu. ft. 3. A candy box is 6 in. square and 2 in. deep. What is its volume? 4. A rectangular piece of wood 4 in. square and 10 in. long contains how many cubic inches? 5. A piece of timber 10 in. square and 1 yd. long contains how many cubic inches? It must be how long to contain 1200 cu. in.? 1350 cu. in.? 1 cu. ft.? 6. A box is 10 in. wide and 10 in. deep, inside measure. What must be its length in order that it may hold 1 bushel? 7. The bottom of a rectangular tin can measures 5 in. by 6 in. How deep must it be to hold 1 gallon? 1. A pile of 4-foot wood, 8 ft. long and 4 ft. high, contains how many cubic feet? 2. A pile of 2-foot wood, 8 ft. long and 4 ft. high, contains how many cubic feet? 3. A pile of 1-foot wood, 8 ft. long and 4 ft. high, contains how many cubic feet? 4. If wood is cut into sticks that are 1 ft. 6 in. long, how many cubic feet are there in a pile 8 ft. long and 4 ft. high? 232. Originally, a cord of wood consisted of 128 cu. ft., or the equivalent of a pile of 4-foot wood, 8 ft. long and 4 ft. high. It is the present custom, however, to consider as a cord any quantity of wood that is equivalent to a pile 8 ft. long and 4 ft. high, whatever may be the length of the sticks. The side of such a pile has a surface of 8 × 4, or 32, square feet. Therefore, To find the number of cords in a pile of wood, multiply its length by its height expressed in feet, and divide the product by 32. 233. Written 1. Find the number of cords in a pile of wood: a. 36 ft. long and 6 ft. high. b. 20 ft. long and 5 ft. high. 2. What must be the length of the sticks in order that 4 cords of wood shall contain: 3. What must be the length of a pile of wood in order that a pile 4 ft. high may contain 51⁄2 cords? 4. What must be the height of a pile of wood in order that a pile 20 ft. long may contain : a. 21 cords? b. 4 cords? c. 17 cords? BUILDING WALLS 234. There are no universal rules for the measurement of masonry. Some masons measure around the outside of a cellar wall to determine its dimensions, while others make allowance for the corners. The method of measurement should be specified in the contract in every case. Quantities of uncut stone are bought by the cord, and usually 99 cu. ft. are taken for a cord. From 21 to 23 bricks 8" x 4" x 2" are estimated to make a cubic foot of brick wall. Some masons estimate the number of bricks required for a wall by multiplying the number of square feet in one side of the wall by 7, when the wall is one brick thick, by 14 when it is two bricks thick, and by 21, when it is three bricks thick, allowing for all openings. A perch of stone or masonry is 243 cu. ft. Concrete walls are estimated by the cubic yard, and the methods of measurement vary. Foundation walls are generally measured without regard to openings. When there are many openings some contractors allow one half for openings, and some make full allowance. 235. Written 1. A retaining wall is 220 ft. long and 8 ft. high. It has an average thickness of 3 ft. Find the cost of the stone used, at $5.40 per cord, a cord of stone making 99 cu. ft. of wall. 2. Find the cost of the brick for a wall 120 ft. long, 121 in. thick, and 40 ft. high, at $6.50 per M., estimating 21 bricks for a cubic foot, and making no allowance for openings. 3. Find the cost, at $9.50 per M., of a brick veneer 4 in. thick on the outside of a house measuring 45 ft. by 30 ft. and 20 ft. high, making an allowance of 200 sq. ft. for doors and windows, and allowing 7 bricks for a square foot of surface. 4. The walls of a rectangular cellar 87 ft. 6 in. by 45 ft. (outside measure), and 9 ft. deep, are 18" thick. Find the cost of the stone at $6.30 per cord, estimating a cord of stone to make 100 cu. ft. of wall, and deducting 18 cu. ft. for corners. 5. Find the cost of 24 concrete pier foundations each 21 in. square and 5 ft. deep, at $5.00 per cubic yard. 6. A garden wall 55 ft. long, 6 ft. high, and 18 in. thick cost how much at $4.20 a perch? 7. A contractor built a concrete cellar wall 54 ft. by 30 ft. (outside measure), 8 ft. high, and 11⁄2 ft. thick, receiving $5 per cubic yard. He used 75 barrels of cement costing $1.80 a barrel, 12 loads of sand costing $1.25 a load, and 50 cu. yd. of crushed stone at $1.30 per cubic yard. How much had he left for labor and profit? FLOOR COVERING 236. A yard of carpet or matting is a yard of the length of the piece, as it is unrolled, regardless of its width. The exact number of yards of material to be purchased for the covering of any given floor is difficult to determine, because of the waste in fitting, and in matching figures. 237. Written 1. If this floor is covered with carpet yd. wide, how many strips, running lengthwise, must be pur 26' 15 purchased for this floor, allowing 1 yd. for waste in matching? 3. A room is 20' x 18'. |