a. Find the volume of the solid bounded by the hyperboloid

and the planes z = 0 and z = h, h > 0.

b. Express your answer in part (a) in terms of h and the areas A₀ and Ah of the regions cut by the hyperboloid from the planes z = 0 and z = h.

c. Show that the volume in part (a) is also given by the formula

where A_m is the area of the region cut by the hyperboloid from the plane z = h/2.

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