A cylinder is inscribed in a cone as shown in the gure. The radius of the cone is 4 inches and the height is 7 inches. (a) Express the volume, V, of the cylinder in terms of the height of the cylinder, h. Hint: You will need ratios for similar triangles. V(h) = (b) Find V'(h) = (c) Find the height that will maximize the volume of the cylinder. h: (d) Find the maximum volume of the cylinder: Give an exact answer in terms of 1:. v