[ENGG. SCI] Determine the centroid of the thin lamina
Answer (1)
1. Rectangle: - The rectangle has a length of 6 and a width of 4. - Area of a rectangle = length × width = 6 × 4 = 24 square units 2. Semicircle: - The diameter of the semicircle is 8 + 6 = 14. - The radius is half the diameter: 14 / 2 = 7 - Area of a circle = π × radius² = π × 7² = 49π - Area of a semicircle = (1/2) × Area of a circle = (1/2) × 49π = (49/2)π square units 3. Total Area: - Total area = Area of rectangle + Area of semicircle = 24 + (49/2)π square units Using π ≈ 3.14159: - Total area ≈ 24 + (49/2) × 3.14159 ≈ 24 + 76.969 ≈ 100.969 square units
