To find the solid contents of a sphere or globe ; Multiply the circumference by the diameter, which will give the superficial content; then multiply the surface by one sixth of the diameter, and the product will be the solidity. The diameter of a globe is 8 feet; what is its solid content? 87:22: 25,142 × 8=201,136 × 1,333=268,114288 ft. Ans. To find how much a round tree, that is equally thick from end to end, will hew to, when made square ; Extract the square root of twice the square of the semidiameter, which root will be the side of the stick when made square. There is a round stick of timber 24 inches in diameter; how large square will it hew? 12 12 144 2 in. 288(16,97 the side of the stick, 1 26)188 156 329)3200 3387) 23900 191 To measure the solidity of any irregular body whose dimensions cannot be taken ; Put the body to be measured into some regular vessel, and fill it with water; then take out the body, measure the fall of water in the vessel, which will be the solidity of the body. Miscellaneous Questions. 2 1. What number added to the thirty first part of 3813, will make the sum 200? Ans. 77. 2. What difference is there between twice 5 and twenty, and twice twenty five? Ans. 20. 3. The remainder of a division is 325, the quotient 467, and the divisor is 43 more than the sum of both; what is the dividend? Ans. 390270. 4. What will 14 cwt. beef cost at 5 cents per pound? Ans. $78,48. 5. In an orchard of fruit trees of them bear apples, pears, plums, 60 of them peaches, and 40 cherries; how many trees does the orchard contain? Ans. 1200. 6. What length must be cut off a board 83 inches broad, to contain a square foot? Ans. 17 inch. 7. A father divided his estate in the following manner; to A. he gave 4 so often as B. had 6, and to C. 7 so often as 9 to D; what was the sum divided if A's share was $600 ? Ans. $2600. 8. A father dying left his son a fortune, of which he ran through in 8 months; of the remainder lasted him 12 months longer, when he had $900 left; what did his father bequeath him? Ans. $2100. 9. A merchant begins the world with $500, and finds that by his distillery he clears $5000, in 6 years; by his navigation, $5000 in 7 years; and that he spends in gaming $5000 in 3 years; how long will his estate last? Ans. 30 years. 10. A. can do a piece of work alone in 7 days, and B. in 12; in what time will both, working together, finish it? Ans. 4 days. 11. A. and B. are on opposite sides of a circular field 268 poles about; they begin to go round it, both the same way at the same instant of time; A. goes 22 rods in 2 minutes, and B. 34 rods in 3 minutes; how many times will they go round the field before the swifter overtakes the slower? Ans. A. 16 times. B. 17 times. 12. A. and B. together can do a piece of work in 20 days; with the assistance of C. they can do it in 12 days, in what time would C. do it by himself? 13. Ans. 30 days. Suppose a cistern has a pipe that conveys 4 galIons, 2 qts. into it in an hour, and another that lets out 2 gallons 1qt. 1pt in an hour; if the cistern contain 84 gallons, in what time will it be filled? Ans. 39 h. 31 m. 4515 sec. 14. If a man spend $22,8125 in one year, what does he spend per day? Ans. $0,0625. 15. A guardian paid $4800, for $3692,309 which he had in his hands 6 years: What rate of interest did he 16. pay Ans. 5 per cent. ? What number is that from which if you take of , and to the remainder add of, the number will be 10? Ans. 1019 17. A water tub holds 73 gallons; the pipe, which conveys the water to it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes. Now, supposing both these to be carelessly left open, and the water to be turned on at 4 o'clock in the morning; a servant, at 6, finding the water running, puts in the tap; in what time, after this accident, will the tub be filled? Ans. 32 min. 58118 sec. 18. A hare starts 12 rods before a hound; but is not perceived by him till she has been up 45 seconds; she scuds away at the rate of 10 miles an hour; and the dog, on 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? Ans. 2288 ft. 97 seconds, 19. Required the number, from which, if 7 be subtracted, and the remainder be divided by 8, and the quotient be multiplied by 5, and 4 added to the product, the square root of the sum extracted, and three fourths of that root cubed, the cube, divided by 9, the last quotient, may be 24? Ans. 103. 20. Two men depart from the same place; the one goes East, and the other North; one goes 20 miles per Ο dav, and the other 25 miles; how far apart are they on the 4th day after their departure? Ans. 128,062 miles. 21. Suppose a lighthouse built on the top of a rock ; the distance between the place of observation and that part of the rock level with the eye, 620 yards; the distance from the top of the rock to the place of observation, 846 yards; and from the top of the light house 900 yards; the height of the light house is required? Ans. 76,77 yds. 22. Sound, uninterrupted, moves at the rate of 1142 feet per second; if the time between the lightning and thunder be one minute, at what distance was the explosion ? Ans. 12,977 &c. miles. 23. If the earth be 7911 miles in diameter, and the moon 2180 miles; how many moons will it take to make one earth? Ans. 47,788. 24. A. sets out for London precisely at the time when B. at Lincoln, sets forward for London, distant 100 miles; after 7 hours they met on the road, and it then appeared, that A. had ridden 11⁄2 mile more than B At what rate an hour did each of them travel? Ans. A. 72, B. 6. 25. There is an island 73 miles in circumference, and 3 footmen all start together to travel the same way around it; A. goes 5 miles a day, B. 8, and C. 10; when will they all come together again? Ans. 73. days. 26. A. B. and C. are to share $48000 in the proportion of,, and . respectively; but C's part being lost by his death, it is required to divide the whole sum properly between them? Ans. A. $27428,5714. B. 20571,4284. 27. A man dying left his wife in expectation that a child would be afterwards added to the surviving family; and making his will, ordered, that, if the child were a son, of his estate should belong to him, and the remainder to his mother; but if it were a daughter, he appointed the mother, and the child the remainder. But it happened, that the addition was both a son and a daughter, by which the widow lost in equity, $2400 more than if there had been only a girl. What would have been her dowry had she had only a son? Ans. $2100. 28. A man died leaving an estate of $1800, which he divided between his three sons in the following manner. They were of 12, 16, and 18 years of age, and were to receive such sums at their father's decease, as put at interest, would give them equal sums, when they arrived What did each one receive? at 21 years of age. 29. When first the marriage not was tied My age with hers did so agree, As nineteen does with eight and three ; What were our ages at marriage? Ans. 57 and 33. AMUSING AND INSTRUCTIVE QUESTIONS. A man bought a piece of ground 30 feet long and 20 feet wide, on which he set a barn and house, each 30 feet long and 20 feet wide; how did he set them? Said Harry to Edmund, I can place four 1's so that, when added, they shall make precisely 12; can you do so too? Says Edmund to Harry, the upper half of a carriage wheel, moves faster than the under half; can you tell me the reason? Charles said, that his instructor asked him if it would take any more boards to build a fence over the top of a hill, than it would to build one of the same height, (by a plumb line) across the base of the same hill: he told his instructer that it would take no more boards; and also that no more trees could grow on a hill, than could grow on its base, or on a piece of ground equal to its base, although the surface of the hill should be double the surface of its base. His instructer told him that he was correct. If a cannon be raised one mile high, with the mouth pointing directly towards the earth, and it be discharged in that position, where will the ball move the swiftest, through the first or last half mile from the cannon's mouth? |