s] The shape of a 20-cm tall flower vase is given by rotatinga curve about the x \text {-axis for } x \in[0,20] . \text { This curve consists of

the graph of } f(x)=5+\frac{1}{2} \sqrt{x} \text { for } x \in[0,16] \text { and the graph of } g(x)=\frac{1}{8}(x-16)^{2}+7 \text { for } x \in[16,20] . \text { Lengths are measured in } \mathrm{cm} \text { and } the base of the vase is at x = 0. (a) Show the shape of the vase by sketching the graphs of f(x) and g(x) in the respectiveintervals given above. What is the radius at the top of the vase? What is the radius at the base? (b) Find the volume of the vase, showing your working.