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Question 1107513: The wafer cone shown in the figure is to hold 12 in3 of ice cream when filled to the bottom. The diameter of the cone is 2 inches, and the top of the ice cream has the shape of a hemisphere. Find the height h of the cone. (Round your answer to two decimal places.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! No picture available, but assume total volume includes the hemisphere.
V= V cone + V hemisphere
12 in^3= (1/3)pi*r^2h+(4/3)(1/2)pi*r^3, r=1, since d=2
12=(1/3)pi*h+(2/3)pi
move (2/3) pi to left and divide both sides by (1/3) pi.
h=9.46 cm.
Check grossly--(1/3)pi*r^2*h is about 9.5, a little more since (1/3)pi>1
V sphere is (4/3)*pir^3=about 4, and half of that is about 2, or a little more
That is 11.5 cm^3, in the range of 12.
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