Question

A hemispherical bowl of radius 5 inches is filled to a depth of h​ inches, where 0less than or equalshless than or equals5. Find the volume of water in the bowl as a function of h.​ (check the special cases hequals0 and hequals5​.)

Answer 1

The shape of the water is that of a "spherical cap." The formula for the volume of a spherical cap is ...

... V = π·h²·(r -h/3) . . . . . . . from web search

For a radius of 5 in, this is

... V = π·h²·(5 -h/3) . . . . in³

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For h=0

... V = π·0²·(5 -0/3) = 0

For h=5 in

... V = π·(5 in)²·((5 -5/3) in) = (2/3)π·5³ in³ . . . . . the volume of a hemisphere of radius 5