Problems from Geography and History 1. In 1845 the United States offered Spain $100,000,000 for Cuba. The area of Cuba is 45,884 square miles. How much per acre was the price offered? 2. The population of Cuba is about 1,600,000. How many acres are there for each inhabitant ? 3. Porto Rico has an area of 3531 square miles. Its population in 1900 was about 1,000,000. How many more people per square mile has Porto Rico than Cuba? 4. In the Hawaiian Islands there are about 14,000 Americans and English, 40,000 Japanese and Chinese, 9000 Portuguese, and 75,000 natives. What is the per cent of each class of the population? 5. The population of the Philippine Islands is about 7,000,000. The total area of the islands is 114,361 sq. mi. About what is the population per square mile? 6. The annual exports from the port of Manila include $8,000,000 of hemp, $6,000,000 of sugar, $2,000,000 of tobacco, $2,500,000 of gold, and $1,250,000 of coffee. Find the average total value of these exports for each inhabitant of the islands. 7. The direct cost of the recent war with Spain was about $130,000,000. If to this sum $70,000,000 more is added for the indirect cost of the war, how much would this make the islands acquired by the war cost per square mile? 8. The total continental territory of the United States is 3,681,661 square miles. The total territory of the groups of islands recently acquired is 124,601 square miles. About what part of the total territory belonging to the country is that of these islands? Review Problems See p. 207. 1. A ball weighing 15 pounds is rolling at the rate of 20 feet a second and meets another ball weighing 12 pounds, coming in the opposite direction at the rate of 10 feet a second. How fast will the larger ball continue to roll after the collision? Find the difference of momentum. 2. Which has the greater amount of momentum, a rifle bullet weighing of an ounce with a velocity of 2000 feet a second, or a 5-pound ball rolling at the rate of 10 feet a second? 3. What is the amount of momentum of a locomotive weighing 60 tons, moving at the rate of 25 miles an hour? 4. How many pounds of continuous force will it take to stop such a locomotive in 2 minutes? Find how much momentum must be overcome each second. 5. How many feet are there in 3 chains and 20 links? 6. How many square rods are there in a field that is 10 ch. 50 li. long and 6 ch. 25 li. wide? 7. Find the number of square feet in a lot that measures 3 ch. 10 li. in width and 5 ch. 30 li, in length ? 8. The surveyors in measuring a rectangular lot of land counted 241⁄2 chains on one side and 324 chains on another. Find how many acres there are in the lot. 9. A rectangular field containing 60 acres measures 24 chains on one side. What is the other dimension? 10. One side of a triangular field measures 25 chains. The perpendicular distance from this side to the opposite angle is 18 chains. How many acres are there in the Spheres AAA See pp. 182, 202, and Book II, p. 244. A sphere may be regarded as composed of a great number of pyramids or cones, having their bases in the surface of the sphere and their vertices at the center. The volume of a sphere is equal to of the product of its surface and its radius. 1. Find the combined volume of 10 equal pyramids, each of whose bases contain 2 square inches, and whose common altitude is 9 inches. 2. What is the diameter of a sphere whose circumference is 314.16 in. ? 3. How many square inches are there in the surface of this sphere? 4. Find the volume of the sphere. 5. What is the surface of a sphere whose diameter is 25 feet? 6. What is its volume ? 7. Find the number of cubic inches in a hemisphere 3 feet in diameter. 8. What is the weight of a sphere of iron 10 inches in diameter, if the specific gravity of the iron is 7.2? 9. If a 10-inch cubical block of wood is turned in a lathe so as to take the form of a sphere, how many cubic inches of the wood are taken off? Miscellaneous Problems 1. Find one of the two equal factors of 1296. 2. Find the length of a square field that contains 2304 sq. rd. 3. Find two equal numbers, the product of which is equal to the product of 12 and 27. When the two means of a proportion are the same, the mean is called a mean proportional between the two extremes. 4:88: 16. 4. Find the value of x in the proportion 5: x = x : 45. x2 = 225. x = √225 = 15. 5. Find a mean proportional between 8 and 200. 12. Two squares are 18 inches and 24 inches long. How long is a square which is as large as both together? 13. What is the hypotenuse of a right triangle whose sides are 28 ft. and 21 ft. ? 14. What is the altitude of a right triangle whose hypotenuse is 17 ft. and base 8 ft.? 15. Two squares are 82 ft. and 18 ft. long. What is the length of a square equal to the difference between them? 16. Find the length of the diagonal of a rectangle which is 80 ft. long and 60 ft. wide. 17. What is the length of a rectangle whose diagonal is 205 ft. and width 45 ft. ? Find the selling price: Find the gain or loss: 9. Cost $200. 10%. Percentage Discounts 20% and 10%. Marked 10% above cost, then reduced 10. Cost $300. Marked 15% above cost, then reduced 13. Cost $160. Marked 15% above cost, then reduced 10%. 14. Cost $40. Marked 25% above cost, then reduced 15%. 15. Cost $75. Marked 333% above cost, then reduced 20%. 16. Cost $500. Marked 12% below cost, then advanced 20%. |