Let W be the region bounded by the following planes: y=z,2y+z=3, and z=0, with 0≤x≤4 1. Plot the three planes. What is the shape of this solid? (i.e. its geometric name). 2. Write the triple integral that computes the volume in the order dydxdz, and compute its value. 3. Compute the volume using geometry and check that you get the same value. 4. Read pages 928-930 in the textbook. Explain the difference between the center of mass and the centroid of a 3 dimensional object. Find the coordinates of the centroid of this body (hint: Compute the y and z coordinate using integrals, but you do not need to compute the x coordinate: What should the x coordinate be by symmetry?) 5. Now assume that the density of this solid is δ(x,y,z)=xy. What is its mass? 6. Compute the center of mass of the solid if the density is δ(x,y,z)=xy. (Now you need to compute 3 integrals). 7. Add the centroid in red to your plot, and the center of mass corresponding to δ(x,y,z)= xy in a different, bright color. Take two screenshots from different angles, so that we see how the two points are placed.