Chapter 9, Problem 70P

Using the method of composite areas, find the centroid of the truncated parabolic complement.

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.

Determine the centroidal coordinates of the plane region by numerical integration.

Determine the centroidal coordinates of the plane region.

Use integration to find the centroidal coordinates for the volume obtained by revolving the area shown about the x-axis.

The sheet metal trough has a uniform wall thickness. Determine the coordinates of its center of gravity.

Compute the centroidal coordinates of the L-shaped region in terms of b and t using the method of composite areas.

Compute the volume of the spherical cap that is formed when the circular segment is revolved about the y-axis.

Verify the centroidal z-coordinate of the pyramid shown in Table 8.3 by integration.