1 foot 6 inches square. I demand how many such stones will pave it ? Ans. 167 stones. 3. There is a room 109,75 feet about, and 9,25 feet high, which is all, (except two windows, each 6 feet 6 inches high, and 5 feet 9 inches broad,) to be hung with tapestry an ell broad. I want to know how many yards will hang said Ans. 83,59 yards. 4. If the axis of a globe be 27,5 inc. I demand the contents, solid and superficial? room ? Ans. 6,3 feet solid, and 16,49 feet superficial. 5. There is the frustum of a globe, the diameter of whose base is 24 inches, and the altitude thereof is 19 inches. I demand the contents, solid and superficial ? Ans. 2785,5520 inches solidity. 1218,9408 inches superficial. 6. If a tree girth 18 feet 6 inches, and 24 feet long, how many tons of timber are contained in that tree? Ans. 12 tons 33 feet 4 inches. 7. There is a cellar to be dug by the floor, whose length is 33 feet 7 inches, and the breadth 18 feet 9 inches: I demand how many floors of earth are in that cellar ? Ans. 11 floors 56 feet. NOTE. 18 feet square, and 1 foot deep, is a floor of earth. 8. There is a roof to be covered with shingles, whose depth on both sides is 35 feet 6 inches, and the length 48 feet 9 inches. How many squares of shingling are contained therein? Ans. 17 squares 30 feet. 9. There is a cone, whose diameter at the base is 42 inc. and the perpendicular height 94 inches, and it is required to cut off two solid feet from the top-end thereof. I demand what length upon the perpendicular must it be cut off? Ans. 40,43 inches. 10. If a square piece of timber be 12 feet long, and if the side of the square of the greater base be 21 inches, and the side of the square of the lesser base 3 inches, how far must I measure from the greater end, to cut off three solid feet? Ans. 22,46 inches. 11. Three men bought a grindstone, of 40 inches diameter, which cost 20 dollars, of which sum the first man paid 9 dollars, the second 6, and the third 5. I demand how much of the stone each man must grind down, proportionally to their money? Ans. 5,17 inches, breadth of ring for the first. 4,83 inches, breadth of ring for the second. 10,00 inches, breadth of ring for the third. R 12. How many feet of square-edged boards, 14 inches thick, including the saw-calf, can be sawn out of a log 20 feet long, and 24 inches diameter ? Ans. 384 feet. RULE. As the thickness of the board, including the sawcalf, is to the solid content, so is 12 inches to the answer. 13. If the diameter of a round tree, (equally thick from end to end,) be 22 inches, and its length 20 feet, I demand how many solid feet it will contain, when hewn square? Ans. 33,6+ feet. RULE. Multiply twice the square of its semidiameter in inches, by the length in feet, and divide that product by 144, and the quotient will be the answer. 14. A gard'ner had an upright cone, The mason said there was a rule Ans. It must be cut at of its height. 15. There is a corn-crib, whose depth is seven-tenths of the width, and the length six times the depth, and the solid capacity is 367 feet. I demand the depth, breadth, and length, and how many bushels of corn it will contain ? Ans. ft. 6 inc. the depth, 5 ft. breadth, 21 ft. length. It will contain 295+ bushels. 16. Suppose, sir, a bushel is exactly round, That bushel is legal all America over. But a workman would make one of another frame; Ans. 19,107 inches diameter. 17. In the midst of a meadow, well cover'd with grass, I took just an acre to tether my ass: How long must the cord be, that, feeding all round, 18. A farmer has a corn-crib 16 feet square, but he has a mind to pull it down, and build a new one large enough to hold three times as much as the old one. I demand how much square the new one must be ? Ans. 28 feet, and near 7 inches. 19. There is a stone 20 inches long, 15 inches broad, and 8 inches thick, which weighs 217 lbs. I demand the length, breadth, and thickness of another of the same kind and shape, which weighs 1000 lbs. ? Ans. Length 33,28 inches, breadth 24,96 inches, and thickness 13,312 inches. 20. If an iron bullet, whose diameter is 4 inches, weighs 9 lbs. what will the weight be of another bullet, of the same metal, whose diameter is 9 inches ? Ans. 102 lbs. 8 oz. 4 drs. 21. There is a square pyramid of marble, each side of its base is 5 inches, and the height thereof 15 inches, and its weight is 12lbs. 4 oz.. I demand the weight of another like square pyramid, each side of whose base is 30 inches? Ans. 2646 lbs. 22. There is a globe of marble, whose diameter is 6 inc. and its weight 11 lbs. What will be the diameter of another globe, of the same marble, that weighs 500 lbs. ? Ans. 21,4 inches diameter. 23. There is a frustum of a pyramid, whose bases are regular octagons: each side of the greater base is 21 inches, each side of the lesser base 9 inches, and its length 15 feet. I demand how many solid feet are contained therein ? Ans. 119,2 solid feet. 24. There is a frustum of a cone, and the diameter of the greater base is 36 inches, the diameter of the lesser base 20 inches, and the length or height 215 inches. I demand the length and solid content of the whole cone, and also the solid content of the given frustum? 94,98 feet. Ans. Content of the whole, Content of the frustum, 78,70 25. If the top-part of a cone contains 26171 solid inches, and 200 inches in length, and the lower frustum thereof 159610 solid inches, I demand the length of the whole cone, and the diameter of each base ? Ans. Length of the whole cone, 384,3 inches. Diameter of the greater base, 42,94 26. There is a frustum of a cone, whose solid content is 20 feet, and its length 12 feet, and the greater diameter bears such proportion to the lesser, as 5 to 2. I demand the diameters ? Ans. The greater diameter is 24,24147 inches, and the lesser 9,69659 inches. 27. There is a wall which contains 18225 cubic feet, and the height is five times the breadth, and the length eight times the height. I demand the length, height and breadth? Ans. Length 180, height-22), and breadth 43 feet. 28. There was a pole, whose top-end was broken off by a blast of wind, and in falling struck the ground at 15 feet distance from the lower end of the pole: the broken piece was 39 feet long. I demand the length of the pole? Ans. 75 feet. By Euclid, book first, 47th proposition, the square of the hypothenuse of any right-angled triangle, is equal to the sum of the squares of the base and perpendicular. 29. A May-pole there was, whose height I would know: Ans. 79,26+ feet. 30. What will be the diameter of a globe, when the soidity and superficial content thereof are equal? Ans. 6. 31. What will be the axis of a globe, when the solidity is in proportion to the superficies, as 18 to 8? NOTE. Nos. 30 and 31 are taken from Algebra. Ans. 23. 32. Suppose a pole on level ground to be 75 feet above the surface, at what height from the ground must I cut it, that the top-end may fall 55 feet from the lower end of the pole, the end where it was cut off resting on the stump or upright part? Ans. 17 feet high. 33. There are three Grenado shells of such capacity, that the second shell will just lie in the concavity of the first, and the third in the concavity of the second. The solidity of the metal of the first shell is equal to its concavity, and the solidity of the metal of the second to the concavity, is as 7 to 5, and the solidity of the third or least shell's metal to its concavity, is as 9 to 4. Now supposing the diameter of the first or greatest shell to be 16 inches, and allowing every solid inch of iron to weigh 4 oz. what is the diameter of the two lesser shells, and the thickness and solidity of the metal of every shell, and the weight of every shell? Ans. Weight of the greatest, 268,08 lbs. of the second, 156,38 lbs. and of the least, 77, 33 lbs. Diameter of the second shell, 12,699 inches, and of the least shell, 9,485 inches. The thickness of the metal of the greatest shell, 1,65 inches, of the second shell, 1,607 inches, and of the third shell, 1,541 inches. 34. I have a joist 7,5 inches wide, and 2,25 inches thick, but I want one twice as large, that will be 3,75 inc. thick. I demand the breadth of such an one? Ans. 9 inc. 35. I have a square stick of timber 18 inches by 14, but one of a third part of the timber in it, provided it be 8 inc. deep, will serve: how wide will it be? Ans. 10,5 inc. 36. I have a plank 16 feet 5 inches long, and I want just a square yard slit off: at what distance from the edge must the line be drawn? Ans. 6114 inches. 37. I have a square garden, whose area is 2500 yards: what is each side of the square, and the breadth of a walk along one side, one end of which may just take up one-half of the square? Ans. One side of the square is 50 yards. 38. What difference is there between one floor 20 feet square, and two others, each 10 feet square? Ans. 200 feet difference. 39. What is the difference between a solid half foot, and half a foot solid? Ans. 648 inches: or the half a foot solid is only the quarter of a solid half foot. 40. A fellow said that when he counted his basket of peaches, 2 by 2, 3 by 3, 4 by 4, 5 by 5, 6 by 6, there was one left; but when he counted them 7 by 7, they came out even. How many peaches had he? Ans. 103. 41. A hare starts 12 rods before a greyhound, and is not perceived by him, till she is up 45 seconds: she scuds away at the rate of 10 miles an hour, and the dog in view makes after her, at the rate of 16 miles an hour. How long will the course hold, and what space will be run over, from the spot where the dog started P Ans. 1 min. 37 sec. and the space ran by the dog was 3 furlongs 18 rods. 42. Suppose I send a man from here. (Washington, G. C.) at 6 o'clock in the morning, to Pittsburgh, distant 100 miles, |