Question 956871
a cone and a hemisphere share the base that is a semicircle with radius 3 and the cone is inscribed inside the hemisphere. find the volume of the region inside the hemisphere
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The base of a hemisphere has to be a circle, not a semicircle.
For the hemisphere,
{{{Vol = 2pi*r^3/3}}}
For the cone,
{{{Vol = pi*r^2*h/3}}}
h = r in this case, so
{{{Vol = pi*r^3/3}}}
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You didn't show where the region is, but it's likely the difference between the 2 volumes.