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 12-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 . DENOMINATE NUMBERS. Capacity. 347. The standard unit of capacity used in measuring liquids is a gallon. A gallon equals 231 cubic inches. 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 (311 gal.), of a rectangular tank 2 ft. by 4 ft. by 12 ft. 4. Find the approximate capacity, in barrels (311 gal.), of a cylindrical cistern 6 ft. in diameter and 6 ft. deep. 5. Find the approximate capacity, in barrels (311⁄2 gal.), of a cylindrical cistern 12 ft. in diameter and 6 ft. deep. 6. Find the approximate capacity, in barrels (311 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 2150.4 cubic inches. 66 NOTE. In measuring large fruits, vegetables, lime, and coal, the unit is the "heaped bushel." A heaped bushel equals about 11⁄2“ stricken bushels." DRY MEASURE. 2 pints (pt.) 1 quart (qt.). 8 quarts 4 pecks = = 1 peck (pk.). = 1 bushel (bu.). A bushel is nearly 14 cubic feet. A "heaped bushel" is about 1 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 2 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 7 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 (14) 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. 16 ounces (oz.) = 1 pound (lb.). The abbreviation for 1 hundredweight (100 lb.) is cut. MISCELLANEOUS WEIGHTS. 1 gallon of water 1 gallon of milk 1 gallon of kerosene 1 cubic foot of water 1 bushel of wheat 1 bushel of beans 1 bushel of clover seed 1 bushel of shelled corn 1 bushel of ear corn 1 bushel of rye 1 bushel of barley 1 bushel of oats = about 81 lb. = about 8.6 lb. = = = about 6 lb. = 62 lb. = 60 lb. = = 60 lb. = 60 lb. = 60 lb. = = = 56 lb. = 70 lb.* = = 56 lb. = 48 lb. = 32 lb. 1. Of 2650 lb. coal at $5.50 per ton. 2. Of 2650 lb. oats at 24¢ a bushel. 3. Of 3330 lb. wheat at 80¢ a bushel. 4. Of 4650 lb. potatoes at 42¢ 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. Find the cost PROBLEMS. 1. Of 2560 lb. hay at $7.50 per ton. 3. Of 2 tons meal at of a cent a pound. (a) Find the sum of the five results. 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. 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.) |