a) The button mushroom is made up of two parts: a top and a stalk. The top is in theshape of an upper hemisphere of radius h. The stalk is in the shape of a cylinder ofheighth with radius a, where a <h. Sketch the button mushroom by placing thebase of the stalk at the origin (0, 0, 0). The whole button mushroom will bealigned symmetrically with respect to the z-axis. b) Formulate all the equations describing the button mushroom and its bound. Labelall the equations on the sketch clearly. c) Hence, formulate the solutions using triple integrals in cylindrical coordinates and find the volume of the button mushroom. [Hint: You may split the volume into two parts, the top and the stalk before adding up].

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