Locate the centroid of the shaded area. (ANS: 3/10 h)
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- The picture board and its triangular supporting bracket form a composite surface. Calculate the height h of the support that minimizes the centroidal z-coordinate of the assembly.Locate the centroid of the volume generated by revolving the area shown about the line AB. Use numerical integration.Determine the centroidal z-coordinate of the curved surface of the half cone by integration.
- Show that every axis passing through the centroid of the equilateral triangle is a principal axis.Using integration, locate the centroid of the area under the n-th order parabola in terms of b, h, and n (n is a positive integer). (b) Check the result of part (a) with Table 8.1 for the case n = 2.Using the method of composite areas, find the centroid of the truncated parabolic complement.
- Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.Use integration to locate the centroid of the volume of the hemisphere. Compare your results with Table 8.3.