SOLUTION: A scoop of ice cream has a diameter of 4.2 cm. It is placed in a cone with a diameter of 4 cm. and a height of 6 cm. If the ice cream melts into the cone, will it overflow the con

Algebra ->  Volume -> SOLUTION: A scoop of ice cream has a diameter of 4.2 cm. It is placed in a cone with a diameter of 4 cm. and a height of 6 cm. If the ice cream melts into the cone, will it overflow the con      Log On


   

Question 138963: A scoop of ice cream has a diameter of 4.2 cm. It is placed in a cone with a diameter of 4 cm. and a height of 6 cm. If the ice cream melts into the cone, will it overflow the cone?
Answer by solver91311(24713) About Me  (Show Source):
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The volume of a sphere is %284%2F3%29pi%2Ar%5E3, so the volume of the scoop of ice cream, presuming a VERY TIDY person serving the ice cream who invariably makes his/her ice cream scoops into absolutely perfect spheres, is %284%2F3%29pi%2A2.1%5E3 (If the diameter is 4.2, the radius must be 2.1). The volume of a right circular cone is 1/3 that of a right circular cylinder with the same base radius and height, so %28pi%2Ar%5E2h%29%2F3. For the given cone: %28pi%2A2%5E2%2A6%29%2F3=pi%2A2%5E2%2A2=pi%2A2%5E3. Don't forget to take some napkins.