Problem
From the figure shown, AB = diameter of circle O₁ = 30 cm, BC = diameter of circle O₂ = 40 cm, and AC = diameter of circle O₃ = 50 cm. Find the shaded areas A₁, A₂, A₃, and A₄ and check that A₁ + A₂ + A₃ = A₄ as stated in the previous problem.
 

Problem
From the figure shown below, O₁, O₂, and O₃ are centers of circles located at the midpoints of the sides of the triangle ABC. The sides of ABC are diameters of the respective circles. Prove that
 

where A₁, A₂, A₃, and A₄ are areas in shaded regions.
 

Problem 719
Determine the centroid of the lines that form the boundary of the shaded area in Fig. P-718.
 

Problem 718
Locate the centroid of the shaded area shown in Fig. P-718.
 

Problem 717
Locate the centroid of the bent wire shown in Fig. P-717. The wire is homogeneous and of uniform cross-section.
 

Problem 716
A slender homogeneous wire of uniform cross section is bent into the shape shown in Fig. P-716. Determine the coordinates of the centroid.
 

Problem 715
Determine the coordinates of the centroid of the area shown in Fig. P-715 with respect to the given axes.
 

Problem 714
The dimensions of the T-section of a cast-iron beam are shown in Fig. P-714. How far is the centroid of the area above the base?
 

Problem 709
Locate the centroid of the area bounded by the x-axis and the sine curve $y = a \sin \dfrac{\pi x}{L}$ from x = 0 to x = L.
 

Problem 708
Compute the area of the spandrel in Fig. P-708 bounded by the x-axis, the line x = b, and the curve y = kxⁿ where n ≥ 0. What is the location of its centroid from the line x = b? Determine also the y coordinate of the centroid.