Charles St. PROBLEMS-AREAS 159 1. The picture represents Boston Common. By use of the scale indicated, find the length of each side and the perimeter of the Common. Beacon St. Tremont St. Boylston St. 1 in.represents mi. 2. It may easily be seen to consist of 1 trapezoid and 3 triangles. Measure the necessary lines by use of the scale and compute the area of each part. 3. Find the total area of the Common. 4. The circle containing a cross indicates the position of the Army and Navy Monument; how far is this monument from Beacon Street? From Boylston Street? 5. Central Park in New York city ismi. wide and 21 mi. long; how many acres does it contain? 6. What is the ratio of the area of Central Park to that of Boston Common? 7. Name some of the forms shown in the map. Park St. 160 PROBLEMS-RAINFALL 1. The following are the records by days of the rainfall at a certain place during September: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2. The adjacent lines in the figure are in. apart; how high is each of the dark columns? How do the heights compare with the records of rainfall in Exercise 1? What numbers in the figure show on what days occurred the various amounts of rain? 3. Find from the diagram the rainfall on the 29th. 4. Robert set out a 2-quart pail and measured the rainfall for April. The records were: Represent the rainfall graphically as in Exercise 2. 5. What is the difference between the greatest and least rainfall for the month? PROBLEMS-REVIEW 161 1. From New York to Boston is 217 miles; how long does it take a train traveling 42 mi. per hour to go from New York to Boston? Express the result to .01 of an hour. 2. A train goes 12 mi. in 16.4 min.; what is the speed per minute to the nearest .01 of a mile? Find the result to the nearest hundredth: 3. 29.5 7.5. 4. 48.6 x 2.7. 6. 11.485 × 2.8. 7. 72.80 5. 856.4321.6. 3,465. 8. 14.2 ÷ 7.25. 9. What fraction of 1 square yard is 12 sq. in.? 144 sq. in.? 156 sq. in.? 156 sq. in.? 288 sq. in.? 10. How many window-curtainsyd. long can be cut from a piece of goods 30 yd. long? Of 500? Of 1,700? Of 4,000? Of 6,400? 20. How many are 20% of 300? 21. How many are 60% of 400? 22. How many are 5% of 700? 23. How many are 100% of 100? 24. How many are 150% of 100? 25. How many are 200% of 100? Of 200? Of 80? Of 5? 26. The table shows the average annual rainfall of various places to September, 1902. Chicago... Boston.. Of 900? 34.8 Sacramento... 20.9 | Pensacola.... 57.1 62.2 41.1 New York City. 44.8 Yuma... 3.0 St. Louis...... Which of these places had the greatest rainfall? The least? What is the difference in inches between these extremes? Find how much the rainfall of each place exceeds the smallest in the list. Find how much the rainfall of each place falls below the greatest in the list. 162 PROBLEMS-REVIEW 1. How much would one pay for 5 yd. of lawn at 331¢ a yard? 2. The picture shows a power-house 60 ft. long and 50 ft. wide; what area does it cover? 3. How many windows are shown? There are twice as many in the whole building. Each window is 3 ft. wide and 10 ft. high; find the total window surface. Add to this 96 sq. ft. for door surface. 4. The side walls are 16 ft. high and the front wall 19 ft. at the highest point; find the total surface of the four walls of the building. 5. Deduct from the total surface of the walls the surface of the windows and doors; what is the surface of the brickwork? 6. The average thickness of the wall is 8 in. In such a wall the number of bricks required to 1 sq. yd. of surface is 135. How many thousand bricks did it take to build the walls of the power-house? 7. Find the ratio of two cubes of edges 3 in. and 5 in. 8. Construct a barometer line from these readings: POWERS AND ROOTS AND MEASUREMENT Powers and Roots 1. What is the volume of a cube 2 in. on a side? 2. What is the volume of a cube 3 ft. on a side? What is this unit for measuring volume called? 3. What is the volume of a cubical block of granite 4 ft. on a side? The computations for finding the volumes of the above cubes are 2 X2 X2=8, 3 x3 x 3 = 27, 4 X 4 X 464. The product of three equal factors is called the cube or the third power of any of the factors. Thus, in the above exercises, 8 is the cube or third power of 2; 27 is the cube or third power of 3; and 64 is the cube or third power of 4. 4. Find the product of 5, 5, and 5. what number? 125 is the cube of 5. Find the product of 6, 6, and 6; of 7, 7, and 7; of 8, 8, and 8. What is the cube of 6? Of 7? Of 8? 6. How many cubic yards of masonry are there in a cubical pier 15 ft. on a side? 7. What is the length of an edge of a cube containing 8 cu. in.? Of one containing 27 cu. in.? 1,728 cu. in.? Each result is seen to be one of the equal factors in the products 2 x2x2 = 8, 3 × 3 × 3 = 27, 12×12×12=1,728. One of the three equal factors of a number is called its cube root. Thus, in the above equations 2 is the cube root of 8, 3 is the cube root of 27, and 12 is the cube root of 1,728. 8. How many inches in the side of a 1-foot cube? 9. What is the cube root of 8? Of 27? Of 64? Of 125? |