7) [20 points] Imagine a microphone-like solid with uniform density (6 = 1) comprised of a cylinder and a half sphere. The cylinder is bounded by the surfaces x? + y? = 1, z = 0, and z - 5. While the half sphere is bounded from above by x2 + y2 + (z - 5)2 - 1 and from below by 2 - 5. a) Sketch the microphone b) Find the moment of inertia of the microphone around the vertical line which passes through the point (0, 1, 0). You may either calculate this directly or using the parallel aris theorem c) Without calculating anything, determine if the moment of inertia will increase, decrease, or stay the same if: i) the microphone is moved one unit in the positive r direction ii) the microphone is moved one unit in the positive y direction iii) the microphone is moved one unit in the positive z direction Explain your reasoning