346. MISCELLANEOUS PROBLEMS. 1. Find the solid content of an octagonal right prism the area of whose base is 24 square inches and whose altitude is 15 inches. 2. What is the solid content of a cylinder or of any right prism, the area of whose base is 30 square inches and whose altitude is 12 inches ? 3. How many cubic feet of earth must be removed to dig a well 6 feet in diameter and 20 feet deep? * 4. Find the approximate number of feet of 13-in. lumber required to make the lining of the sides of a cylindrical silo that is 20 feet in diameter and 30 feet deep. 5. Find the approximate number of cords of rough stone in a cylindrical pile that is 16 feet in diameter and six feet deep. 6. Find the approximate number of brick necessary for a solid cylindrical foundation that is 9 feet in diameter and 4 feet high. 7. If the average specific gravity of the brick and mortar used in the foundation described in problem 6, is 1.9, how much does the entire foundation weigh? 8. Find the weight in kilograms of a column of water 1 decimeter square and 10 meters deep. 9. Find the weight in pounds of 1000 feet of white pine 1-inch boards, the specific gravity being .6. 10. Find the weight of a load (1 cubic yard) of wet sand, the specific gravity being exactly 2. (P. 375.) * The exact number of cubic feet cannot be expressed in figures. An approximation that will answer many practical purposes may be obtained by regarding the circle (base) as of its circumscribed square. If an answer more nearly accurate is required use .78 instead of 4. DENOMINATE NUMBERS. Capacity. 347. The standard unit of capacity used in measuring liquids is a gallon. A gallon equals 231 cubic inches. Liquid Measure. = 1 gallon (gal.). 31) gallons = 1 barrel (bbl.). Observe that 1 cubic foot = nearly 71 gallons. Observe that 4.2 cubic feet = nearly 1 barrel. A kerosene barrel contains about 52 gallons. It equals nearly 7 cubic feet. PROBLEMS. 1. Find the capacity (approximate or exact), in gallons, of a rectangular tank 3 ft. by 4 ft. by 8 ft. 2. Find the approximate capacity, in gallons, of a cylindrical tank 4 feet in diameter and 4 feet deep. 3. Find the approximate capacity, in barrels (31) gal.), of a rectangular tank 2 ft. by 4 ft. by 12 ft. 4. Find the approximate capacity, in barrels (31) gal.), of a cylindrical cistern 6 ft. in diameter and 6 ft. deep. 5. Find the approximate capacity, in barrels (311 gal.), of a cylindrical cistern 12 ft. in diameter and 6 ft. deep. 6. Find the approximate capacity, in barrels (31] gal.), of a cylindrical cistern 12 ft. in diameter and 12 ft. deep. (P. 376.) Denominate Numbers — Capacity. 348. The standard unit of capacity used in measuring grain, fruits, vegetables, lime, coal, etc., is a bushel. A bushel equals 2150.44 cubic inches. NOTE. - In measuring large fruits, vegetables, lime, and coal, the unit is the “heaped bushel.” A heaped bushel equals about 14“ stricken bushels." DRY MEASURE. 2 pints (pt.) = 1 quart (qt.). = 1 bushel (bu.). A “heaped bushel" is about 14 cubic feet. A“ dry gallon ” (4 quarts dry measure) equals 268.8 cubic inches. Enough ear corn” to make, when shelled, one bushel, occupies about 24 cubic feet. If the corn is inferior in quality it will occupy more space than this — sometimes 2 cubic feet. PROBLEMS. 1. Find the capacity in bushels of a wheat bin 8 ft. by 8 ft. by 10 ft.* 2. Give the dimensions of the smallest bin in which 1000 bushels of oats may be stored. 3. In a bin 12 feet square, there is rye to the depth of 71 feet. How many bushels ? 4. How many bushels of potatoes (without heaping the bin) may be stored in a bin that is 8 ft. by 4 ft. by 6 ft. ? 5. If the corn is of excellent quality, how many bushels of “shelled corn” may be expected from a crib of ear corn, 8 ft. by 10 ft. by 80 ft. ? (P. 377.) * For many practical purposes the approximate ratio (11) of the bushel to the cubic foot will give, in such problems as these, results sufficiently accurate. Denominate Numbers — Weight. 349. The standard unit of weight in common use is a pound Avoirdupois. AVOIRDUPOIS WEIGHT. 2000 pounds =1 ton (T.). MISCELLANEOUS WEIGHTS. 1 gallon of water = about 8} lb. = 60 lb. - 56 lb. = 48 lb. 1 bushel of oats = 32 lb. 1 barrel of flour = 196 lb. 1 barrel of beef or pork = 200 lb. PROBLEMS. Find the cost1. Of 2650 lb. coal at $5.50 per ton. 2. Of 2650 lb. oats at 244 a bushel. 3. Of 3330 lb. wheat at 80$ a bushel. 4. Of 4650 lb. potatoes at 424 a bushel. (a) Find the sum of the four results. * This means the amount of ear corn required to make 1 bushel of shelled corn. Denominate Numbers — Weight. PROBLEMS. 1. Of 2560 lb. hay at $7.50 per ton. per cwt. (a) Find the sum of the five results. Find the cost 6. Of 2140 lb. oats at 24¢ a bushel. (b) Find the sum of the five results. Find the cost 11. Of 520 lb. clover seed at $6.30 a bushel. (c) Find the sum of the five results. Find the approximate weight 16. Of a barrel of kerosene. 17. Of 1 quart of milk. 18. Of the oats that will fill a bin that is 4 ft. by 4 ft. by 9 ft. 19. Of the water that will fill a tank that is 2 ft. by 2 ft. by 12 ft. 20. Of a five-gallon can of kerosene. (P. 378.) |