50. At 10 cents a square foot, what is the cost of lining a cylindrical tank (curved surface and bottom) whose diameter is 10 feet and whose depth is 12 feet? 51. A sphere is exactly and a cone exactly of a cyl inder of the same dimensions. Find the solid content and compare the following: (a) A 6-inch cube. (b) A cylinder 6 in. in diameter and 6 in. long. (c) A 6-inch sphere. (d) A cone; base 6 in. in diameter, altitude 6 in. 52. A cubic foot of steel weighs 490 lb. (a) What is the weight of a cylinder of steel 1 foot in diameter and 1 foot long? (b) Of a sphere of steel 1 foot in diameter? (c) Of a cone of steel, base 1 foot in diameter, altitude 1 foot? 53. A circular piece of land 20 rods in diameter contains more or less than 2 acres? 54. At sight, give approximate answers to the following: (c) Interest of $250 for 1 yr. 8 mo. 5 da. at 6% ? (i) Interest of $1200 for 6 da. at 8% ? (j) Interest of $600 for 20 da. at 4% ? (k) Interest of $397.28 for 2 yr. 6 mo. at 6% ? (1) Interest of $5000 for 5 mo. 29 da. at 8% ? (m) Interest of $3000 for 2 mo. 29 da. at 7% ? (n) Interest of $4000 for 3 mo. 29 da. at 6% ? 55. At sight, give answers to the following, that are true to dollars; then, with the aid of a pencil, if necessary, obtain answers that are true to cents. (a) Cost of 2970 lb. coal at $4.50 per ton?1 1 2970 ib. is nearly 1 tons. 2 What is the cost of 3500 at $12 per ton? 3 At $10 a ton, how much does 1 lb. cost? 4 At $15 per M., how much is 1 foot worth? 5 6740 brick are nearly 63 M. 6200 lb. butter at 274 cents is worth how much? 7 At 24¢ a bushel, 1 lb. of oats is worth how much? 6 MISCELLANEOUS PROBLEMS. NOTE. The following problems are selected mainly from sets of examination questions supplied to the author for this purpose by one hundred school principals and superintendents. 10 1. Each edge of a cube is diminished by of its length. (a) By what fraction of itself is the volume diminished? (b) By what fraction of itself is the surface diminished? 2. How many cubical blocks, each edge of which is ft., are equivalent to a block 8 ft. long, 4 ft. wide, and 2 ft. thick? 3. A ladder 78 ft. long stands perpendicularly against a building. How far must it be pulled out at the foot that the top may be lowered 6 ft. ? 4. A merchant sold 3 of a quantity of cloth at a gain of 20% and the remainder at cost. (a) His gain was what per cent of the cost? (b) If he gained $7.29 what was the cost of the goods? 5. What must I pay for 4% stock to get 5% on the investment? 6. The cubical content of one cube is eight times that of another: (a) How does an edge of the first compare with an edge of the second? (b) How does the surface of the first compare with the surface of the second? 7. A creditor receives $1.50 for every $4.00 that is due him and thereby loses $301.05. (a) What was the sum due him? (b) What per cent of the debt did he lose? 8. At $20 per M., board measure, what is the cost of the following: A stick of timber 30 feet long and 14 inches square, and a plank 18 feet long, 8 inches wide, and 21 inches thick? 9. A and B hire a pasture for $85; A puts in 8 cows and B puts in 12 cows. How much should each pay? 10. Simplify the following: of 7 of 11. 11. Seven times John's property plus $32200 equals 21 times his property. How much is he worth? 12. Two men engage in business with a joint capital of $5000. The first year's gain was $1760, of which one received $1056. How much capital did each furnish? 13. Thirty-five per cent of the men in a regiment being sick, only 637 men were able to enter battle. How many men were there in the regiment? 14. A lawyer collected 80% of a debt of $2360 and charged 5% commission on the sum collected. How much Idid the creditor receive? 15. Write a negotiable note for $500, making yourself the payee and James J. Rogers the maker. Interest at the legal rate. 16. A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1035. How much did he invest? 17. What is the rate per cent per annum if $712 gains $142.40 in 3 yr. 4 mo.? 18. A person asked for a lot of land, 40% more than it cost him, but finally reduced his price 15% of his asking price and sold it, making $9.50. (a) What per cent did he make? (b) How much did the land cost him? (c) How much did he receive for it? 19. Purchased stock at a premium of 8 per cent. What rate of interest do I receive on the investment if it pays an annual dividend of 6% ? 20. Find the volume of a cube the area of whose surface is 100.86 square inches. 21. How many apples must a boy buy and sell to make a profit of $9.30, if he buys at the rate of 5 for 34 and sells at the rate of 4 for 3¢? 22. Find the cost of 1875 lb. hay at $6.50 per ton. 23. What is the interest on $1200 from Sept. 21, 1898, to May 5, 1899, at 7% per annum? 24. The area of a square field is 10 acres. What is the distance diagonally across the field? 25. A " drummer" earns $2500 a year. One thousand dollars of this sum is a guaranteed salary. The remainder is his commission of 5% on his sales. What is the amount of his annual sales? 26. The area of a triangle is 325 square inches. Its base is 25 inches. What is its altitude? 27. Gave 63 lb. butter, worth 364 a pound, for 31 gal. oil. What was the cost of the oil per gallon? 28. A can build a certain wall in 10 days; B can build it in 12 days, and C in 15 days. In how many days can they build the wall working together? 29. A horse and a carriage together cost $550. The horse cost as much as the carriage. Find the cost of each? 30. A man willed of his property to his wife, of the remainder to his daughter, and the rest to his son. The difference between the wife's portion and the son's portion was $12480.33. How much was the man worth? |