Exercise 1. If a circular arc is 100 yards long and the angle at the center is 45°, what is the diameter of the circle? 2. If a circular arc is 4 feet long and the diameter of the circle is 12 feet, what is the angle at the center? 3. Assuming the radius of the earth to be 4000 miles, find the length of a degree of longitude; of a degree of latitude. 4. What fractional part of the circumference of a circle is intercepted by radii which meet at an angle of 30°? of 45° ? of 60°? of 90° ? 5. What decimal part of the area of a circle is the area of the square inscribed in the circle? 6. Through how many degrees of latitude does the state of California extend if its length from north to south is 750 miles? 7. Through how many degrees of longitude does California extend if its western extremity is 600 miles west of its eastern? 8. Through how many degrees of longitude does Alaska extend if it is 3000 miles between its eastern and western extremities? 9. If a foot racer runs 100 yards on a one-mile circular track, what angle at the center of the track will be made by joining it with the points where he starts and finishes? 10. How many degrees in the angle made by two radii which intercept an arc equal in length to the radius? Where a greater degree of accuracy is desired, the following method is used. Rule. To find the circumference of a circle, multiply the diameter by π (about 3.1416). c = 3.1416 d. EXAMPLE 1. Find the circumference of a circle whose diameter Find the circumferences of circles with radii as follows: 25. If the diameter of an automobile wheel is 36 inches, how many revolutions does it make in going 10 miles? (Use π = 22.) 26. What is the diameter of a rope whose circumference is 3 inches? 27. If the diameter of the earth's equator is 7927 miles, what is its length? 28. What is the circumference of the circle that can be inscribed in a square 12 feet on a side? Area Rule. To find the area of a circle, multiply the square EXAMPLE 2. Find the area of a circle whose diameter is 6 inches. EXAMPLE 3. Find the radius of a circle if its area is 2463 sq. ft. Find the areas of circles with radii as follows: Find the areas of circles with diameters as follows: 25. What is the area of a cross section of a water pipe that is 3 inches in diameter? 26. What is the diameter of a circular plot of ground whose area is one acre? 27. What is the radius of a circle whose area is one half an acre? Circumference of circle = 12 × 3.1416 37.699 ft. Arc of sector= = 14 = = 1 × 1.47 × 6 = 4.41 sq. ft. Exercise 1. In a circle whose diameter is 3 ft., determine the area of a sector whose arc is 30°. 25" 9" Ellipses 2. In a circle whose diameter is 10 ft., determine the area of a sector whose arc is 25°. 3. In a circle whose diameter is 14 ft., determine the area of a sector whose arc is 42°. 4. A kite is made of the shape shown in the diagram, the semicircle having a radius of 9 in., and the kite a total height of 34 in. Find the area of the kite. 5. A 10-inch fan opens out into a sector whose angle is 130°. What is the area of the opened fan? d 1 |