As shown in the illustration, a section of standard weight seamless steel pipe, has an external diameter of 6.6 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.
• A 90° bend is one-quarter of a full circle, so its angle in radians is important for arc-length calculations. • Arc length along a curve is given by arc length = radius × angle (in radians). • For a bent pipe, the outer radius and inner radius differ by exactly the pipe’s outside diameter, regardless of the bend radius shown in the illustration.
• Express 90° in radians, then think about how much longer a circle with a larger radius is compared to one with a smaller radius when they subtend the same angle. • Write an expression for the length of the outer arc and for the inner arc, then subtract them and simplify; notice what cancels out. • Check whether you actually need the bend radius from the illustration, or only the pipe’s given outside diameter, to find the difference in arc lengths.
• Convert 90° to radians correctly before using it in the arc length formula. • Confirm that the difference between outer and inner radii equals the given pipe diameter (6.6 in). • After computing the difference in arc lengths, compare your numeric result carefully with the closest answer choice, watching for rounding.
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