How to find the centroid of the quarter circle of radius 1 with center at...
How to find the centroid of the quarter circle of radius 1 with center at the origin lying in the first quadrant?
Answer & Explanation
Beginner2023-03-04Added 6 answers
Non-Calculus Solution: Observation 1: The centroid must lie along the line (otherwise the straight line running through (0,0) and the centroid would be to "heavy" on one side). Observation 2: For some constant, c, the centroid must lie along the line and furthermore, c must be less than 1 since the area of the triangle formed by the X-axis, Y-axis and is more than half of the area of the quarter circle. Observation 3: Since the area of the quarter circle (with radius = 1 is the line must divide the quarter circle into 2 pieces each with area . The area of the triangle formed by the X-axis, the Y-axis, and is Thus
and the centroid is located at the midpoint of the line segment
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