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- Use integration to locate the centroid of the volume of the hemisphere. Compare your results with Table 8.3.Use integration to locate the centroid of the shaded region in terms of R and t. (b) Show that when t0 the result of part (a) agrees with that given in Table 8.2 for a quarter circular arc.Compute the surface area of the axi-symmetric domed structure.
- Using the method of composite areas, find the dimension h that maximizes the centroid coordinate y of the plane region shown.Use numerical integration to locate the centroid of the symmetric planeUsing 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.
- Determine the centroidal coordinates of the plane region by numerical integration.Locate the center of gravity of the hammer if the mass of the steel head is 0.919 kg, and the mass of the hardwood handle is 0.0990 kg.A 6-in. diameter hole is drilled in the conical frustum. Calculate the volume and the surface area of the resulting body.
- Determine the centroidal z-coordinate of the curved surface of the half cone by integration.The 12-ft wide quarter-circular gate AB is hinged at A. Determine the contact force between the gate and the smooth surface at B due to water pressure acting on the gate. Use =62.4lb/ft3 for water.Determine the smallest distance I) that would prevent the concrete dam from tipping about corner A. Use w=62.4lb/ft3 for water and c=150lb/ft3 for concrete.