Question #3: Find the (x,y) coordinates of the centroid of the shaded area between the semi-circle and the inscribed triangle: R Circular.

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter9: Moments And Products Of Inertia Of Areas
Section: Chapter Questions
Problem 9.43P
Question
**Question #3:** Find the (x,y) coordinates of the centroid of the shaded area between the semi-circle and the inscribed triangle:

*Diagram Description:*

1. **Semi-circle**:
   - The semi-circle is displayed with its flat edge lying along the horizontal axis.
   - The radius of the semi-circle is denoted by \( R \).

2. **Inscribed Triangle**:
   - A triangle is inscribed within the semi-circle.
   - The base of the triangle coincides with the flat edge of the semi-circle.
   - The vertex of the triangle opposite the base lies at the center of the semi-circle's flat edge.
   - The height of the triangle from the center of the flat edge (base) to the top point is denoted by \( Y \). 

3. **Shaded Area**:
   - The shaded area is the space found between the semi-circle and the inscribed triangle.
   - This area is highlighted in orange color.

The task is to calculate the coordinates of the centroid of this orange shaded area.
Transcribed Image Text:**Question #3:** Find the (x,y) coordinates of the centroid of the shaded area between the semi-circle and the inscribed triangle: *Diagram Description:* 1. **Semi-circle**: - The semi-circle is displayed with its flat edge lying along the horizontal axis. - The radius of the semi-circle is denoted by \( R \). 2. **Inscribed Triangle**: - A triangle is inscribed within the semi-circle. - The base of the triangle coincides with the flat edge of the semi-circle. - The vertex of the triangle opposite the base lies at the center of the semi-circle's flat edge. - The height of the triangle from the center of the flat edge (base) to the top point is denoted by \( Y \). 3. **Shaded Area**: - The shaded area is the space found between the semi-circle and the inscribed triangle. - This area is highlighted in orange color. The task is to calculate the coordinates of the centroid of this orange shaded area.
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