Q.3: Find the fraction of the face centered cubic unit cell volume filled with hard spheres as shown in figure below if the total volume of cell (cubic) is 729 cm.

5.) see photo for question

For the part below that consists of a semicircle on top of a rectangle, with r = 4 in and h=9 in, determine: a. Centroid x and y [in] b. Area moment of inertia I [in] 2r

Consider the beam cross-section and the direction of moment (shown in side view) applied as shown in Figure Q2. All dimensions are in mm. Note the square hole in the cross-section. (a) Locate the neutral axis of the beam cross-section (y-coordinate from the bottom of the section). Please draw a larger schematic and neatly label all distances for calculating the neutral axis. (b) What is the area moment of inertia of the cross-section with respect to the neutral axis? (c) If the applied bending moment M=5kN.m, then determine the maximum bending stress (absolute value, tensile or compressive) anywhere on the beam.