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Question 707278: I have a punchbowl in the shape of a hemisphere with radius 9 inches. From that FULL BOWL, I am filling cylindrical glasses with the diameter of 3 inches and height of 4 inches. How many glasses can I fill? Please show or explain if can.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! The volume of the punchbowl is
V = (1/2)*(4/3)*pi*r^3 ... this is half of the volume of the sphere formula
V = (1/2)*(4/3)*3.14*9^3
V = 1,526.04
So the volume of the punchbowl is approximately 1,526.04 cubic inches. So it can hold up to 1,526.04 cubic inches of liquid.
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Volume of cylindrical glass
V = pi*r^2*h
V = 3.14*1.5^2*4 ... note: diameter = 3 --> radius = 3/2 = 1.5
V = 28.26
Each glass holds approximately 28.26 cubic inches of fluid.
So if you've completely filled the punchbowl and you want to fill each glass completely, then you will be able to fill 1526.04/28.26 = 54 glasses completely until you would need to refill the punchbowl.
Note: in the real world, you won't be able to fill something completely without spilling liquid. So keep in mind that the punchbowl will have slightly less liquid than 1526.04 cubic inches of liquid. This means that you'll have less punch to serve up. Also, each glass won't be completely filled to the top, which will allow you to fill a few more glasses because you'll have extra punch.
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