As shown in the illustration, a section of standard weight, seamless steel pipe, has an external diameter of 3.8 inches. When the pipe, is bent into a 90 degree turn, the length of the outside edge of the curve "A-B" will exceed the length of the inside edge of the curve "C-D" by __________. See illustration GS-0108.
• Use the arc length formula for a circle: Arc length = radius × angle (in radians) • Recognize that points A–B and C–D lie on concentric arcs of a 90° bend (same angle, different radii) • Note that the difference in radii between the outside and inside edges of the pipe equals the outside diameter of the pipe, 3.8 inches
• How can you express the outer arc length and inner arc length separately using radius and angle, then subtract them? • When you subtract the two arc-length expressions, what happens to the unknown bend radius? • What angle in radians should you use for a 90° (right-angle) bend, and how do you apply it to the diameter of the pipe?
• Convert 90° to radians correctly before using the arc length formula • Be sure the difference in radius between the outer and inner arcs is the full outside diameter, not the radius • After computing the numerical result, compare carefully to the choices and check if it is reasonable in size compared to the 3.8-inch diameter
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