WRITTEN EXERCISES 246. 1. Find the area of a rectangle 16 ft. by 5 ft. 3 in. Since the length and width must be expressed in like units, 5 ft. 3 in. is first changed to feet. Then the number of square feet in the area is found by 247. A solid having six rectangular faces is called a rectangular solid. 248. A rectangular solid whose faces are equal squares is called a cube. A cube each of whose faces is a square inch is called a cubic inch. Describe a cubic foot; other cubic units. 249. If each cube in this rectangular solid represents some cubic unit, each row represents 4 of those units, each layer 2 × 4 of them, and since there are 3 layers, the rectangular solid contains 3 x 2 x 4 cubic units, or 24 cubic units. The number of cubic units that any solid contains is called its volume. 250. If the length, width, and thick ness of a rectangular solid are expressed in inches, the volume is found by multiplying the number of inches in the length by the number of inches in the width and that product by the number of inches in the thickness, calling the result cubic inches. If all the dimensions are in feet, the volume is found by finding their product and calling the result cubic feet. Stated more briefly: The volume of a rectangular solid is equal to the product of its length, width, and thickness, all expressed in like units. A rectangular solid 4 ft. by 2 ft. by 3 ft. has a volume of 24 cu. ft. WRITTEN EXERCISES 251. 1. Find the volume of a rectangular solid 12 ft. by 8 ft. 6 in. by 4 ft. 4 in. SOLUTION 442 cu. ft. Length = 12 ft.; width = 81 ft.; thickness = Since the dimensions must be expressed in like units, 8 ft. 6 in. and 4 ft. 4 in. are first changed to feet. Then the number of cubic feet in the volume is obtained by finding the product of 12, 81, and 4}. 8. A rectangular solid is 14 ft. 5 in. by 6 ft. 7 in. by 9 ft. 11 in. Find its volume to the nearest .001 of a cubic foot. SUGGESTION. The dimensions may be reduced to inches. Then the volume in cubic inches may be changed to cubic feet. Find the volume of each of the following rectangular solids to the nearest .001 of a cubic foot: 9. 23 ft. 8 in. long, 11 ft. 5 in. wide, 5 ft. thick. 10. 21 ft. 7 in. long, 16 ft. 1 in. wide, 4 ft. thick. 11. 35 ft. 10 in. long, 13 ft. 4 in. wide, 6 ft. 5 in. thick. THIRD PROG, AR. - 10 12. Some of the land near the Bank of England is valued at £75 per square foot. Find the value of a piece of this ground 42 feet by 60 feet. 13. Air is about oxygen. How many cubic feet of oxygen ft. by 10 ft.? are there in a room 16 ft. by 13 14. How many pressed brick 8 in. long and 2 in. thick, laid on edge, are required to pave a street 2310 ft. by 30 ft.? 15. Find the cost, at 55¢ per square yard, of constructing a stone road in New Jersey, 15 ft. wide and 6 mi. 1980 ft. long. 16. How many pounds of blasting powder are required to blast out a tunnel 9 ft. square and 440 yd. long through solid rock, if 1 pound will loosen 3 cu. yd. of rock? 17. Find the weight of a box of dynamite whose contents measure 4 ft. by 21 ft. by 3 ft., if 1 cubic foot weighs 1031 lb. 18. The floors of a warehouse were designed to carry 250 pounds per square foot as a maximum load. Find the maximum load for a floor 62 ft. by 36 ft. 19. How many rubber erasers 2 in. long, 14 in. wide, and in. thick can be cut from a block of India rubber 1 ft. 6 in. by 1 ft. 3 in. by 9 in.? 20. Find the area of a large illustration on the front page of a periodical 114 in. wide and 164 in. long, if the side margins of the page are in. each, the bottom 14 in., and the top 34 in. 21. Find the number of cubic inches of space in a chest in. thick, if the outside dimensions are 22 in., made of wood 19 in., and 11 in. 22. A drill for sowing wheat covered 24 acres of ground per day. How long did it take to sow a field 216 rd. by 160 rd.? 23. A reaper used in a Minnesota wheat field cuts a swath 18 feet wide. How far must it go in a straight line to reap an acre of wheat? OPERATIONS WITH DENOMINATE NUMBERS 252. Addition, subtraction, multiplication, and division with denominate numbers are performed just as with other numbers. It is necessary, however, to bear in mind the number of units of any denomination required to make a unit of the next higher denomination. 5. Add 2 T. 5 cwt.; 1 T. 12 cwt.; 4 T. 15 cwt.; 3 T. 8 cwt. 6. Subtract 3 T. 17 cwt. from 10 T.; 22 T. 14 cwt. from 25 T.; 17 lb. 11 oz. from 42 lb. 7. Multiply 12 ft. 8 in. by 6; 2 yd. 27 in. by 4. 8. Divide 85 ft. 8 in. by 4; 181 ft. 8 in. by 7. 9. How much less than a right angle is 77° 42'? 10. How much less than 2 right angles is 154° 28' 33''? Add: 11. 6 lb. 402.15 pwt. and 2 lb. 7 oz. 9 pwt. 12. 14° 17' 15"; 62° 40' 32"; 24° 0' 54"; 41° 50' 19". 13. £865 48. 8d.; £82 98. 101d.; £48 188. 51d. 14. £642 38. 2d.; £66 0s. 61d.; £34 158. 3d. 15. Subtract each amount of money in exercise 14 from the amount written above it in exercise 13. 16. Find of 16° 32' 30"; of 16° 32' 30''; of 125 ft. 4 in. 17. Find 5 times 11 lb. 10 oz.; § of 11 lb. 10 oz. 18. How long was it from June 26, 1893, to May 15, 1906? yr. mo. da. 1906 5 15 1893 6 26 12 10 19 The later date is written as the minuend and the earlier date as the subtrahend, the number of the month being used instead of its name. Subtract as in denominate numbers, considering 30 days as a month and 12 months as a year. The remainder is the difference in time as accurately as it can be expressed in years, months, and days. Find the time from to-day to the following dates: 25. Find the difference in elevation between Lake Huron, 576 ft. 9 in. above sea level, and Lake Superior, 602 ft. 11 in. above sea level. 26. The leakage from a 63-gallon hogshead of rock candy sirup was 2 qt. 1 pt. How much sirup remained? 27. If a passenger locomotive consumes 86 lb. 9 oz. of coal per mile, how much coal will be consumed on a trip of 95 miles? 28. A man picked 93 bu. 6 pk. of cranberries in 12 days. What quantity did he pick per day, on the average? 29. If a skillful operator stamps the name on 24 gross 4 dozen pens per hour, how many will he stamp in 9 hours? |