IX. Curious Comparisons. 1. If a pig whose girth is 2 feet, weighs 50 lb., what is the weight of a similarly proportioned pig whose girth is 4 feet? 2. If a disk of dough 15 inches in diameter is sufficient for 20 doughnuts, how many such doughnuts can be made from a disk 30 inches in diameter ? 3. The bore of a 10-inch gun is how many times as large as the bore of a 2-inch gun ? 4. The ball of a 10-inch gun is how many times as large as the ball of a 2-inch gun? 5. A square, a pentagon, a hexagon, an octagon, and a circle have equal perimeters. (a) Which has the greatest ? area? (b) Which has the least area 6. The capacity of a cistern 6 feet in diameter and 6 feet deep is about 40 barrels. What is the capacity of a cistern 12 feet in diameter and 12 feet deep? 7. A 24-inch pipe is how many times as large as a 1-inch pipe? 8. If a man 6 feet tall weighs 190 lb., how much would a similarly proportioned giant 12 feet tall, weigh? 9. In a certain orchard the trees are 15 feet apart each way and there are 800 trees. How many trees in an orchard of equal size, the trees being 30 feet apart each way? 10. A ball of yarn 3 inches in diameter is sufficient for one mitter. How many mittens can be made from a ball 6 inches in diameter ? 11. A grindstone was originally 30 inches in diameter. It has been worn until it is but 15 inches in diameter. What part of the stone has been worn away? 12. A square and an oblong have equal areas. Which has the greater perimeter ? X. Practical Approximations. Without the aid of a pencil (except for writing results) give approximate answers, sufficiently accurate for many practical purposes, to the following problems: 1. What is the area of a circle 20 inches in diameter ? 2. What is the volume of a 12-inch globe? 3. What is the circumference of a circle that is 40 rods in diameter ? 4. What is the capacity, in gallons, of a tank 6 ft. by 5 ft. by 2 ft.? 5. Is the capacity of a cylindrical pail 6 inches in diameter and 5 inches deep, more or less than a gallon? 6. A piece of land 41 rods by 24 rods is how many acres? 7. What is the capacity in barrels (31 gal.) of a tank 4 ft. by 4 ft. by 2 ft.? 8. What is the weight of one cord of green hickory wood? 9. What is the weight of a stick of seasoned white pine timber 12 in. by 12 in. and 30 feet long? 10. What is the weight of the water that will fill a cylindrical tank that is 8 feet in diameter and 8 feet deep? 11. A circular-mile race track encloses how many acres? 12. If the six-foot drive wheel of a locomotive makes 840 revolutions in moving a certain distance, how many revolutions will a seven-foot wheel make in moving the same distance? 13. Twenty-four kilometers is how many miles? 14. Forty-two kilograms is how many pounds? 15. A 2-inch rainfall makes how many barrels of water to the acre? 16. A certain roof is 40 feet long and, measured horizontally, 24 feet in width. A 2-inch rain-fall should give how many inches in depth in a cistern that receives the water from this roof, the cistern being 6 feet long and 4 feet wide? XI. Puzzling Problems. 1. If a person traveling as expeditiously as possible from Boston to San Francisco, should mail a letter to his friend in Boston every day at noon, how often would the letters be received in Boston? 2. If a man and a boy, the boy doing exactly one-half as much work as the man, can hoe one and one-half acres of corn in one and one-half days, how many acres can 6 men hoe in 6 days? 3. John and James sold apples together. The first day they sold 60 apples at the rate of 5 apples for 2 cents, and received 24 cents. The second day they divided the apples. John took 30 of the larger apples and sold them at the rate of 2 for 1 cent. James took the remaining 30 apples and sold them at the rate of 3 for one cent. They received 25 cents. Why did they receive one cent more the second day than the first? 4. A pile of four-foot wood stands upon a hill-side. The pile is 8 feet long (measured on the ground), and 4 feet high (measured vertically). Does the pile contain one cord? 5. A man had shingles enough to cover his house if he laid them 4 inches to the weather. He laid them 4 inches to the weather. What part of the shingles provided remained? Explain. 6. If on a line of railroad connecting Chicago and San Francisco one passenger train leaves Chicago daily at 6 o'clock A.M., and makes the journey to San Francisco in exactly five days, and one train leaves San Francisco daily at 6 o'clock P.M., and makes the journey to Chicago in exactly five days, (a) a person taking the train at Chicago will meet how many passenger trains while going to San Francisco? (b) How many trains of passenger cars required to equip the road? Carefully paste this sheet upon card-board; then cut |