193. 1. If 48 yd. of cloth cost $62.40, how much will 72 yd. cost at the same rate? 2. If 31 acres of land cost $146.90, how much will 271 acres cost at the same rate? 3. If 51⁄2 tons of coal cost $42.90, how much will 3 tons cost at the same rate? 4. If 4.3 tons of hay cost $53.75, how much will 17.2 tons cost at the same rate? 5. If the profit on .4 of an acre of land is $5.20, what is the profit on 4.4 acres at the same rate? 6. If a man's income is $220 for 2 months, how much is it for one year at the same rate? 7. If a train moves 130 miles in 3 hr. 20 min., at the same rate how far will it move in 7 hr. 40 min. ? 8. If 27 acres of land yield 1512 bushels of oats, how many bushels may be expected from 63 acres? 9. If sugar sells at the rate of 21 lb. for $1, how much should be paid for 125 lb. ? 10. If coffee sells at the rate of 41⁄2 lb. for one dollar, how much should be paid for 63 lb. ? 11. If 15 dozen of eggs will pay for 48 lb. of sugar, how much sugar should be given for 35 dozen eggs? 12. If 25 lb. butter will pay for 36 lb. coffee, how much coffee should be given for 17 lb. butter? 13. Thirty-five bushels potatoes at 35¢ a bushel will pay for how many tons of coal at $7 a ton? 14. Five cords of wood at $5.50 a cord, will pay for how many bricks at $7 a thousand? 15. A ton of oats at 24 a bushel will pay (a) for how much bran at $10 a ton? (b) for how much cottonseed meal at $28 a ton? 194, 195. 1. The diameters of two circles are as 4 to 5. Compare their areas. 2. The diameters of two spheres are as 4 to 5. Compare their solid contents. 3. The area of a 6-inch circle is how many times as great as the area of a 4-inch circle? 4. The solid content of a 6-inch sphere is how many times as great as the solid content of a 4-inch sphere? 5. The circumference of a 6-inch circle is how many times as great as the circumference of a 4-inch circle? 6. The circumference of a 6-inch sphere is how many times as great as the circumference of a 4-inch sphere? 7. If it costs $3 to make a circular excavation 6 feet in diameter and 5 feet deep, how much would it cost at the same rate per cubic foot removed, to make a circular excavation 8 feet in diameter and 5 feet deep? 8. The depth of two round cisterns is the same; but the diameter of one of them is 8 feet and of the other 10 feet. Compare them as to capacity. 9. I am thinking of two 10-foot iron rods. is of an inch in diameter and the other Compare them as to weight. 10. I am thinking of two small iron balls. is of an inch in diameter and the other Compare them as to weight. One of them of an inch. One of them of an inch. 11. I am thinking of two grindstones of equal thickness. One is 15 inches in diameter and the other 20 inches. Compare them as to weight. 12. A makes bricks that are 10% thicker, 10% wider, and 10% longer than those made by B. (a) Compare the bricks as to amount of material. (b) Compare them as to surface. 200. 1. If 5 men can do a piece of work in 18 days, how long will it take 12 men to do a similar piece of work? 2. If 20 men can do a piece of work in 3 days, how long will it take 16 men to do a similar piece of work? 3. If a piece of land 12 rods square is worth $460, what is the value at the same rate of a piece 18 rods square? 4. If a 4-inch metallic ball weighs 8 pounds, what is the weight of a 12-inch ball of the same material? 5. If a 3-foot square marble slab weighs 400 lb., what is the weight of a 4-foot square marble slab, the thickness being the same in each case? 6. If a 2-foot square iron slab 2 inches thick weighs 300 lb., what is the weight of a 3-foot square iron slab 3 inches thick? 7. The opening in a 24-inch sewer pipe is how many times as large as the opening in a 5-inch sewer pipe? 8. The opening in a 14-inch gas pipe is how many times as large as the opening in a 1-inch gas pipe ? 9. How many acres in a rhomboidal piece of land whose length (base) is 96 rods, and whose width (altitude) is 90 rods? 10. How many acres in a trapezoidal piece of land, the length of the parallel sides being 48 rods and 53 rods respectively, and the width (altitude) being 27 rods? 11. How many acres in a piece of land in the form of a triangle whose base is 78 rods and whose altitude is 36 rods 5 feet? 12. How many acres in a rectangular piece of land, the length of the field being twice its breadth, and its perimeter being 240 rods? 206. 1. (a) Of what number are 2, 2, 3, 3, 5, 5, the prime factors? (b) What is the square root of the number? 2. (a) Of what number are 2, 2, 2, 3, 3, 3, 5, 5, 5, the prime factors? (b) What is the cube root of the number? 3. Resolve the number 1764 into its prime factors. What is its square root? 4. Resolve the number 27225 into its prime factors. What is its square root? 5. Resolve the number 1800 into its prime factors. Is this number a perfect square? 6. Is the number 3600 a perfect square? 7. Resolve the number 27000 into its prime factors. What is its cube root? 8. Resolve the number 13824 into its prime factors. What is its cube root? 9. Resolve the number 8640 into its prime factors. Is this number a perfect cube? 10. Which of the following common fractions are perfect squares? 225, 111, 1225, 325, 1617. 184 36 625 11. Which of the following decimals are perfect squares? .64, .144, .0144, .0196, .09, .009, .0009, .0625. 12. Find the square root of (a) 1969, (b) 3025. 1089' 169 13. Find the square root of (a) 121, (b) 18. 2401 14. Find the square root of (a) .1225, (b) .002025. 15. Find the square root of (a) .1849, (b) .0576. 16. Find the cube root of (a), (b) 128. 216 17. Find the cube root of (a) 184, (b) 512 1000 18. Find the cube root of (a) .729, (b) .001331. 19. Find the cube root of (a) .081, (b) .000343. 210. 1. The area of a certain square floor is 7056 feet. How many feet in the perimeter of the floor? 2. The perimeter of a certain square floor is 148 feet. What is its area? 3. The area of a certain square field is 3136 square rods. Find the length of its side. 4. Mr. Tarble's farm is square and contains 221 acres. Find the length of its side. How 5. Mr. Judd's farm is in the form of a rectangle and is twice as long as it is wide. It contains 314 acres. long is it? Find 6. Mr. Snow's farm is in the form of a rectangle. Its length is 11 times its breadth. It contains 933 acres. its perimeter. Its 7. Mr. Miller's farm is in the form of a rectangle. length is three times its breadth. Its perimeter is one 8. There are 121 square inches in one face of a cube. How many cubic inches in its solid content? 9. There are 1350 square inches in the surface of a cube. How many cubic inches in its solid content? 10. The number expressing the cubic inches in the solid content of a certain cube is seven times as great as the number expressing the square inches in the area of one face of the same cube. Find the solid content of the cube. 11. A certain rectangular solid is twice as wide as it is thick and twice as long as it is wide. It contains 2744 cubic inches. Give its dimensions. 12. A certain rectangular solid is twice as wide as it is thick and twice as long as it is wide. The area of its surface is 252 square inches. Give its dimensions. |