709 Centroid of the area bounded by one arc of sine curve and the x-axis
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.
April 2012
708 Centroid and area of spandrel by integration
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.
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707 Centroid of quarter ellipse by integration
Problem 707
Determine the centroid of the quadrant of the ellipse shown in Fig. P-707. The equation of the ellipse is $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$.
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706 Centroid of quarter circle by integration
Problem 706
Determine the centroid of the quarter circle shown in Fig. P-706 whose radius is r.
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705 Centroid of parabolic segment by integration
Problem 705
Determine the centroid of the shaded area shown in Fig. P-705, which is bounded by the x-axis, the line x = a and the parabola y2 = kx.
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Centroids and Centers of Gravity
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Center of gravity of a homogeneous flat plate
Centroids of areas
Centroids of lines
Center of gravity of bodies
Centroids of volumes
Back to topCentroids of Composite Figures
$W \, \bar{x} = \Sigma wx$
$W \, \bar{y} = \Sigma wy$
$A \, \bar{x} = \Sigma ax$
$A \, \bar{y} = \Sigma ay$
$L \, \bar{x} = \Sigma lx$
$L \, \bar{y} = \Sigma ly$
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Center of Gravity of Bodies and Centroids of Volumes
$W \, \bar{x} = \Sigma wx$
$W \, \bar{y} = \Sigma wy$
$W \, \bar{z} = \Sigma wz$
$V \, \bar{x} = \Sigma vx$
$V \, \bar{y} = \Sigma vy$
$V \, \bar{z} = \Sigma vz$
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Example 7 | Area inside the square not common to the quarter circles
Problem
The figure shown below is composed of arc of circles with centers at each corner of the square 20 cm by 20 cm. Find the area inside the square but outside the region commonly bounded by the quarter circles. The required area is shaded as shown in the figure below.
Area inside the larger circle but outside the smaller circle
Problem
From the figure shown below, DE is the diameter of circle A and BC is the radius of circle B. If DE = 60 cm and AC = 10 cm, find the area of the shaded region.
