There were 5 1/2 cups of cranberry juice in the fridge. If Greg frank 2/3 of the juice. How much did he drink?
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Consider the top half of a sphere centered at the origin with radius 
, which can be described by the equation
and consider a plane
with
. Call the region between the two surfaces 
. The volume of is given by the triple integral
Converting to polar coordinates will help make this computation easier. Set
Now, the volume can be computed with the integral
You should get
and consider a plane
with
Converting to polar coordinates will help make this computation easier. Set
Now, the volume can be computed with the integral
You should get
