SOLUTION: scoop of ice cream has a radius of 2 inches and it fits exactly in a cone with the same radius . how tall would the cone that holds this scoop need to be to hold all the icecream i

Algebra ->  Volume -> SOLUTION: scoop of ice cream has a radius of 2 inches and it fits exactly in a cone with the same radius . how tall would the cone that holds this scoop need to be to hold all the icecream i      Log On


   

Question 934400: scoop of ice cream has a radius of 2 inches and it fits exactly in a cone with the same radius . how tall would the cone that holds this scoop need to be to hold all the icecream if it melts?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
You can evaluate the volume, and then use formula for volume of a cone to calculate the unknown height.

Cone: you know r for radius but do not know h for height.

system%28v=%281%2F3%29h%2Api%2Ar%5E2%2Cv=%284%2F3%29%2Api%2Ar%5E3%29

The volumes, v, are equal.

%281%2F3%29%2Api%2Ah%2Ar%5E2=%284%2F3%29%2Api%2Ar%5E3

h%2Ar%5E2=4r%5E3

h=4r%5E3%2Fr%5E2

highlight%28h=4r%29, using then r=2, find h=8.