a. Find the volume of the solid bounded by the hyperboloid and the planes z = 0

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


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 formulaimage


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

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Thomas Calculus Early Transcendentals

ISBN: 9780321884077

13th Edition

Authors: Joel R Hass, Christopher E Heil, Maurice D Weir

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