A figure is formed by removing a semicircle of diameter 14 cm from a quarter circle of radius 14 cm. The diameter of the semicircle lies along one of the straight edges of the quarter circle. Find the perimeter of the figure. (Take π = 22/7.)
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Worked Solution
Step 1: Quarter-circle arc = ¼ × 2 × π × 14 = ¼ × 2 × (22/7) × 14 = 22 cm.
Step 2: One straight radius (untouched by the cut) = 14 cm.
Step 3: Semicircle arc forming the new inner boundary = ½ × π × 14 = ½ × (22/7) × 14 = 22 cm. The diameter of the cut-out is now INTERIOR — it is not on the perimeter.
Step 4: Total perimeter = 22 + 14 + 22 = 58 cm.
Answer: 58 cm
Correct answer: 58 cm
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