(a) Show that the volume of a segment of height
(See the figure.)
(b) Show that if a sphere of radius
where
(c) Using the formula for the volume of a segment of a sphere, it can be shown that the depth
where
(d) A hemispherical bowl has radius 5 inches and water is running into the bowl at the rate of 0.2 in
(i) How fast is the water level in the bowl rising at the instant the water is 3 inches deep?
(ii) At a certain instant, the water is 4 inches deep. How long will it take to fill the bowl?
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Calculus (MindTap Course List)