605 6.1 Radian Measure 111. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if u = 40.0° and r = 152yd. 112. Irrigation Area Suppose that in Exercise 111 the angle is halved and the radius length is doubled. How does the new area compare to the original area? Does this result hold in general for any values of u and r? 113. Arc Length A circular sector has an area of 50 in.2. The radius of the circle is 5 in. What is the arc length of the sector? 114. Angle Measure In a circle, a sector has an area of 16 cm2 and an arc length of 6.0 cm. What is the measure of the central angle in degrees? 115. Measures of a Structure The figure illustrates Medicine Wheel, a Native American structure in northern Wyoming. There are 27 aboriginal spokes in the wheel, all equally spaced. (a) Find the measure of each central angle in degrees and in radians in terms of p. (b) If the radius of the wheel is 76.0 ft, find the circumference. (c) Find the length of each arc intercepted by consecutive pairs of spokes. (d) Find the area of each sector formed by consecutive spokes. U r 116. Area Cleaned by a Windshield Wiper The Ford Model A, built from 1928 to 1931, had a single windshield wiper on the driver’s side. The total arm and blade was 10 in. long and rotated back and forth through an angle of 95°. The shaded region in the figure is the portion of the windshield cleaned by the 7-in. wiper blade. Find the area of the region cleaned to the nearest tenth. 10 in. 958 7 in. 117. Circular Railroad Curves In the United States, circular railroad curves are designated by the degree of curvature, the central angle subtended by a chord of 100 ft. Suppose a portion of track has curvature 42.0°. (Data from Hay, W., Railroad Engineering, John Wiley and Sons.) (a) What is the radius of the curve? (b) What is the length of the arc determined by the 100-ft chord? (c) What is the area of the portion of the circle bounded by the arc and the 100-ft chord? 118. Land Required for a Solar-Power Plant A 300-megawatt solar-power plant requires approximately 950,000 m2 of land area to collect the required amount of energy from sunlight. If this land area is circular, what is its radius? If this land area is a 35° sector of a circle, what is its radius?
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