SOLUTION: If the two equal-sized scoops of ice cream melt completely into the cone, will they overflow the cone? The diameter of the ice cream scoop is equal to the diameter of the cone’s

Question 1153242: If the two equal-sized scoops of ice cream melt completely into the cone, will they overflow the cone? The diameter of the ice cream scoop is equal to the diameter of the cone’s opening. Assume that there is no additional ice cream within the cone. Explain your answer. If the ice cream overflows, approximately how much ice cream will overflow? If the ice cream does not overflow, how much room will be approximately left in the cone? Round to the nearest hundredth.

need help with the problem
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Depends on the dimensions of the cone.
Specifically, the depth or height of it.

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!

Depends on the dimensions of the cone, specifically the height of it.
Since dimensions are not given, we can say that if her ice cream melts of the ice cream will overflow out of the cone only if the volume of ice cream scoops is same as the volume of the cone.
Assume the ice cream scoop is a sphere of radius inches and then the top of the cone will also have radius inches.
Suppose the height of the cone is inches. You need to find out if the volume of the scoops of ice cream is equal the volume of the cone.

the volume of the scoops (spheres ):

the volume of the cone:

........solve for
........simplify

=>
If her ice cream melts of the ice cream will overflow out of the cone only if .
only if both volumes are same:

.

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