7. 16 cu. yds. 26 cu. ft. 1,596 cu. in.? 8. 19 cu. ft. 789 cu. in.? 149. 1. What are the contents of a rectangular solid 6 ft. long, 4 ft. wide, and 3 ft. thick? EXPLANATION: A solid 6 ft. long, 1 ft. wide, and 1 ft. thick contains 6 cu. ft. A solid 6 ft. long, 4 ft. wide, and 1 ft. thick contains 4 times 6 cu. ft., or 24 cu. ft. A solid 6 ft. long, 4 ft. wide, and 3 ft. thick contains 3 times 24 cu. ft., or 72 cu. ft. 2. What is the volume of a rectangular solid 9 ft. long, 5 ft. wide, and 4 ft. thick? 3. How many cubic yards of earth must be removed in digging a cellar 38 ft. long, 26 ft. wide, and 6 ft. deep? 4. How many cubic feet of water will a rectangular cistern hold that is 8 ft. square and 18 ft. deep? 5. How many gallons does such a cistern hold, there being 231 cu. in. in a gallon? 6. How many cubic feet of air are there in a room 18 ft. long, 16 ft. wide, and 9 ft. high? 7. How many cubic inches are there in a block of granite 6 ft. 4 in. long, 4 ft. 3 in. wide, and 2 ft. 10 in. thick? How many cubic feet? 8. How many 1-in. cubes could be sawed from a 3-ft. cube, if there were no waste in sawing? 9. A pile of bricks, solid, is 10 ft. long, 8 ft. wide, and 6 ft. high. How many bricks are there in the pile, a brick being 8 in. long, 4 in. wide, and 2 in. thick? 10. A rectangular block of marble which contains 72 cu. ft. is 6 ft. long and 4 ft. wide. How many feet thick is it? (A block 6 ft. long, 4 ft. wide, and 1 ft. thick contains 24 cu. ft.) 11. The end of a rectangular piece of timber which contains 768 cu. in. is 8 in. long and 6 in. wide. What is the length of the piece of timber? 12. What is the length in feet of a piece of timber which contains 11,232 cu. in., the ends being rectangles 8 in. long and 6 in. wide? 13. From a cellar 36 ft. taken 3,780 cu. ft. of earth. cellar? 150. Wood Measure. long and 21 ft. wide was What is the depth of the 16 cubic feet TABLE. =1 cord foot (cd. ft.). 8 cord feet, or 128 cubic feet, =1 cord (cd.) The typical form of a cord of wood is a compact pile 8 ft. long, 4 ft. wide, and 4 ft. high. In such a pile every foot in length contains 1 cd. ft. 151. EXERCISES. 1. How many cords are there in a pile of wood 24 ft. long, 8 ft. wide, and 6 ft. high? (Solve without figures; first suppose the pile to be 4 ft. wide and 4 ft. high.) 2. How many cord feet in a pile of wood 28 ft. long, 12 ft. wide, and 8 ft. high? How many cords? How many cord feet in 1 ft. of length? A pile of wood containing 45 cd. is 60 ft. long and 16 ft. wide. How high is it? 3. 4. What must be the length of a load of wood 51 ft. wide and 3 ft. high to contain 1 cd.? 5. How many cubic inches are there in 4 cd. and 16 cd. ft.? 6. How many cubic inches in a pile of wood 10 ft. long, 6 ft. wide, and 5 ft. high? How many cords? 7. At $5 a cord, what is the value of the wood that can be piled under a shed 48 ft. long, 24 ft. wide, and 12 ft. high? 152. Lumber Measure. The unit of lumber measure is the board foot, which contains 144 cu. in. Hence, 1 cu. ft. contains 12 board feet. Lumber that is less than an inch thick is counted an inch thick. If it is more than an inch thick, the excess is usually counted. EXERCISES. 153. How many feet of lumber are there in: 1. 28 boards, 18 ft. long, 8 in. wide, and 1 in. thick? 2. 3. 8 joists, 16 ft. long, 6 in. wide, and 2 in. thick? 6 sills, 24 ft. long, 8 in. wide, and 6 in. thick? 4. 60 rafters, 2 in. by 4 in., 10 ft. long? 5. 36 boards, 10 in. wide and 20 ft. long? 6. 12 beams, 30 ft. long, 8 in. wide, and 10 in. thick? 7. Find the cost of the following bill of lumber, at $18 per M feet: 46 boards, 12 in. wide and 18 ft. long; MEASURES OF CAPACITY. 154. Liquid Measure. The standard unit of liquid measure is the gallon, which contains 231 cu. in. NOTE: In measuring the capacity of cisterns, reservoirs, etc., 31 gals. make a barrel (bbl.), and 63 gals. a hogshead (hhd.); but in commerce, the barrel and the hogshead vary in capacity. 155. 1. ORAL EXERCISES. How many gills in 8 pts.? In 12 pts.? In 15 pts.? In 6 pts. 2 gi.? In 9 pts. 3 gi.? 2. How many pints in 9 qts.? In 14 qts.? In 16 qts.? In 7 qts. 1 pt.? 3. How many quarts in 10 gals.? In 16 gals.? In 7 gals. 2 qts.? In 9 gals. 3 qts.? 4. How many quarts in 18 pts.? In 23 pts.? In 30 pts.? 5. How many gallons in 24 qts.? In 30 qts.? In 36 qts.? In 45 qts.? 6. In 50 pts. of kerosene how many quarts? How many gallons? 7. What is a 6-gal. can of milk worth, at 5 cts. a quart? |