A scoop of ice cream has a 1.5 inch radius. How tall is the ice cream cone of the same radius be in order to contain all of the ice cream inside the cone

  6 inches

Step-by-step explanation:

The formula for the volume of a sphere is ...

  V = (4/3)πr^3

The formula for the volume of a cone is ...

  V = (1/3)πr^2h

The volumes will be equal when their ratio is 1:

  (4/3πr^3)/(1/3πr^2h) = 1

  4r/h = 1 . . . . simplify

  4r = h = 4(1.5 in) = 6 in . . . . . multiply by h, substitute given values

The height of the cone must be 6 inches to hold the volume of the spherical scoop of ice cream.

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