high, and the number of square feet in the surface of the room? Ans. 6000 solid feet. 2200 square feet. 16. What are the contents of a triangular prism, whose length is 20 feet, and the three sides of its triangular end or base 5, 4, and 3 feet ? Ans. 120 feet. 17. What are the solid contents of a cone, whose height is 30 feet, and the diameter of its base 5 feet ? Ans. 196.3+ feet. 18. The largest of the Egyptian pyramids is square at its base, and measures 693 feet on a side. Its height is 500 feet. Now, supposing it to come to a point at its vertex, what are its solid contents, and how many miles in length of wall would it make, 4 feet in height and 2 feet thick ? Ans. 80,041,500 cubic feet. 1894.9 miles in length. 19. Required the convex surface of a cone, whose side is 50 feet, and the circumference at its base 12 feet. Ans. 300 feet 20. Required the solid contents of Bunker Hill monument, whose height is 220 feet, and being 30 feet square at its base, and 15 feet square at its vertex. Ans. 115500 cubic feet. 21. What are the contents of a stick of timber 20 feet long, and the diameter at the larger end 12 inches, and at the smaller end 6 inches ? Ans. 9.163-+ feet. 22. What is the solidity of a sphere, whose diameter is 20 inches ? Ans. 4188.8+ inches. 23. What is the convex surface of a globe, whose diameter is 20 inches ? Ans. 1256.6+ inches. 24. What are the contents of a spherical segment 3 feet in height, cut from a sphere 10 feet in diameter ? Ans. 113.0976 feet. 25. What is the solidity of a segment of a sphere, its height being 8 inches, and the diameter of its base 20 inches ? Ans. 1224.7232 inches. 26. How large a cube may be inscribed in a sphere 10 inches in diameter ? Ans. 5.773+ inches. 27. How many wine gallons will a cubical box contain, that is 8 feet long, 4 feet high, and 3 feet wide ? Ans. 718.1+ gallons. 28. How many bushels of grain will a box contain, that is 12 feet long, 5 feet wide, and 4 feet high ? Ans. 192.8+ bushels. 29. What are the contents of a cask, in wine gallons, whose bung diameter is 30 inches, head diameter 24 inches, and length 40 inches ? Ans. 108.19+ gallons. 30. How many cubic feet in a stick of timber, which is 40 feet long, and whose girt is 60 inches ? Ans. 621 feet. Section 51. MISCELLANEOUS QUESTIONS. 1. What is the difference between 7 pence and 10 cents? Ans. £d. 2. What number is that, to which, if } be added, the sum will be 71 ? Ans. 73. 3. What number is that, from which, if 39 be taken, the remainder will be 41 ? Ans. 735 4. What number is that, to which, if 34 be added, and the sum divided by 54, the quotient will be 5 ? Ans. 23. 5. From 11 of a mile take f of a furlong. Ans. 4fur. 12rd. 8ft. 8in. 6. From 7 acres take it of a rood. Ans. 6A. 3R. 7p. 74ft. 36in. 7. John Swift can travel 7 miles in g of an hour, but Thomas Slow can travel only 5 miles in ; of an hour. Both started from Danvers at the same time for Boston, the distance being 12 miles. How much sooner will Swift arrive in Boston than Slow ? Ans. 1244 seconds. 9. If of a ton cost $ 49, what cost lcwt. ? Ans. $ 3.92. 9. How many bricks, 8 inches long, 4 inches wide, and 2 inches thick, will it take to build a wall 40 feet long, 20 feet high, and 2 feet thick ? Ans. 43200 bricks. 10. How many bricks will it take to build the walls of a house, which is 80 feet long, 40 feet wide, and 25 feet high, the wall to be 12 inches thick ; the brick being of the same dimensions, as in the last question ? Ans. 159300 bricks. wide, many acres ? 11. How many tiles, 8 inches square, will cover a floor 18 feet long, and 12 feet wide ? Ans. 486 tiles. 12. If it cost $ 18.25 to carry 11cwt. 3qr. 19lbs. 46 miles, how much must be paid for carrying 83cwt. 2qr. 11lbs. 96 miles ? Ans. $ 267.127047. 13. A merchant sold a piece of cloth for $ 24, and thereby lost 25 per cent. ; what would he have gained, had he sold it for $ 34 ? Ans. 61 per cent. 14. Bought a hogshead of molasses, containing 120 gallons, for $30; but 20 gallons having leaked out, for what must I sell the remainder per gallon to gain $ 10 ? Ans. $ 0.40. 15. In a piece of land 1174 rods long, and 112 rods how Ans. 82A. IR. 18p. 2yd. 7ft. 133 in. 16. Bought a quantity of goods for $ 128.25, and, having kept them on hand 6 months, for what must I sell them to gain 6 per cent. ? Ans. $ 140.02. 17. If 27 bushels of potatoes cost $8.75, what must be paid for 36 bushels ? Ans. $ 11.66+. 18. How many bushels of oats, at 50 cents per bushel, must I give Moses Webster for 93 bushels of corn, at $ 1.25 Ans. 2324 bushels. 19. How many bushels of salt, at $ 1.30 per bushel, must be given in exchange for 75 bushels of wheat, at $ 1.25 per bushel ? Ans. 72,6 bushels. 20. If a sportsman spend of his time in smoking, * in gunning,” 2 hours per day in loafing, and 6 hours in eating, drinking, and sleeping, how much remains for useful purposes? Ans. 2 hours. 21. If a lady spend I of her time in sleep, } in making calls, į at her toilet, 4 in reading novels, and 2 hours each day in receiving visits, how large a portion of her time will remain for improving her mind, and domestic employments ? Ăns. 3 hours per day. 22. What will a piece of land 7f rods long, and 54 rods wide, come to at $ 25,75 per acre ? Ans. $ 6.65111 23. If 5% ells English cost $ 15.16, what will 71+ yards Ans. $ 155.39. 24. If a staff 4 feet long cast a shadow 5 feet, what is the height of that steeple whose shadow is 150 feet ? Ans. 1074 feet. per bushel ? cost ; 25. Borrowed of James Day $ 150 for six months ; afterwards I lent him $ 100 ; how long shall he keep it to indemnify him for the sum he lent me ? Ans. 9 months. 26. A certain town is taxed $ 6045.50 ; the valuation of the town is $293275.00; there are 150 polls in the town, which are taxed $ 1.20 each. What is the tax on a dollar, and what does A. pay, who has 4 polls, and whose property is valued at $ 3675 ? Ans. $ 0.02. A.'s tax $ 78.30. 27. What is the value of 97 pigs of lead, each weighing 2cwt. 3qr. 111b., at £3. 178. 9d. per cwt. ? Ans. £ 1074. Os. 627 d. 28. What is the interest of $ 17.86, from Feb. 9, 1840, to Oct. 29, 1842, at 75 per cent. ? Ans. $35.24 +29. What is the interest of $ 97.87, from Jan. 7, 1840, to Sept. 25, 1842, at 9 per cent. ? Ans. $ 23.92+. 30. T. Jones' note for $ 1728 is dated March 1, 1836 ; Sept. 25, 1836, was received $ 50.00, Jan. 1, 1837, do. $ 60.00 June 7, 1837, do. $ 8.00, Dec. 25, 1837, do. $ 10.00, March 6, 1838, do. $5.00, Sept. 1, 1938, do. $ 9.00, Jan. 1, 1839, do. $ 300.00, July 4, 1839, do. $ 100.00, Sept. 6, 1840, do. $ 14.00, Jan. 25, 1841, do. 8 500.00, Dec. 11, 1841, do. $ 15.00, March 9, 1842, do. $ 200.00, What is due Nov. 29, 1842 ? Ans. $ 1060.29. 31. $ 1000. Salem, N. H., Oct. 29, 1836. For value received, I promise to pay Luther Emerson, Jr., or order, on demand, one thousand dollars with interest. Emerson Luther. Attest, Adams Ayer. On this note are the following indorsements. Jan. 1, 1837, was received $ 125.00, June 5, 1837, do. $ 316 00, Sept. 25, 1837, do. $ 417.00, April 1, 1838, do. $ 100.00, July 7, 1838, do. $ 50.00; What is due, at compound interest, Oct. 29, 1842 Ans. $ 53.79. 32. J. Ladd's garden is 100 feet long and 80 feet wide; he wishes to enclose it with a ditch 4 feet wide; how deep must it be dug, that the soil taken from it may raise the surface one foot. Ans. 51; feet. 33. How many yards of paper, that is 30 inches wide, will it require to cover the walls of a room, that is 151 feet long, 114 feet wide, and 7 feet high ? Ans. 5517 yards. 34. Charles Carleton bas agreed to plaster the above room at 10 cents per square yard; what will be his bill ? Ans. $6.549. 35. How many cubic inches are contained in a cube, that may be inscribed in a sphere 40 inches in diameter? Ans. 12316.8+ inches. 36. The dimensions of a bushel measure are 184 inches wide, and 8 inches deep ; what should be the dimensions of a similar measure, that would contain 4 quarts ? Ans. 91 inches wide, 4 inches deep. 37. A gentleman willed of his estate to his wife, and I of the remainder to his oldest son, and of the residue, which was $.151.33}, to his oldest daughter ; how much of his estate is left to be divided among his other heirs ? Ans. $ 756.66%. 38. A man bequeathed 4 of his estate to his son, and } of the remainder to his daughter, and the residue to his wife ; the difference between his son and daughter's portion was $ 100 ; what did he give his wife ? Ans. $ 600.00. 39. A young man lost of his capital in speculation ; he afterwards gained $500 ; his capital then was $1250; what was the sum lost ? Ans. $ 250.00. 40. From 7 of a yard, there was sold J of it ; how much remained ? Ans.yard. 41. Sold a lot of shingles for $ 50, and by so doing I gained 124 per cent. ? what was their value ? Ans. $ 44.444. 42. If tallow be sold at 7d. per lb., what is the value of 17cwt. 3qr. 18lbs. ? Ans. $208.954. 43. If i of a yard cost $5.00, what quantity will $17.50 purchase ? Ans. 1 yard. 44. If a man travel 17rd. 10ft. in 17 of an hour, how far will he travel in 8 hours ? Ans. 1 mile, 9284 feet. |