Chapter 9, Problem 111P

Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.

Find the centroid of the truncated parabolic complement by integration.

Determine the centroidal z-coordinate of the curved surface of the half cone by integration.

Determine the dimension b of the square cutout so that Ixy=0 for the region shown.

The properties of the unequal angle section are Ix=80.9in.4,Iy=38.8in.4, and Iu=21.3in.4. Determine Ixy.

Compute Ix and Iy for the region shown.

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.

The coordinates of the centroid of the line are = 332 and = 102. Use the first Pappus Guldinus theorem to determine the area, in m2, of the surface of revolution obtained by revolving the line about the x-axis. The coordinates of the centroid of the area between the x-axis and the line in Question 9 are = 357 and = 74.1. Use the second Pappus Guldinus theorem to determine the volume obtained, in m3, by revolving the area about the x-axis.

(a) Find the centroidal axes (coordinates xc and xs) of the given composite area. (b) Determine ly of the composite area about its y-centroidal axis found in part (a). Enter the ly value as the answer in the Respondus answer-box. y 1 in 5 in 3 in 2 in 3 in 3 in 6 in X