The more ice cream that is in immediate contact with air, the faster it will melt. A lower surface area to volume ratio speeds melting because the air can share its heat energy with more of the ice cream at one time. Imagine how much easier it is to for an ice cream flake to melt than a ball of ice cream. For the ice cream to completely melt, the air has to share its heat energy with the ice cream on the surface and the ice cream on the surface has to share its heat energy with the ice cream in the interior of the flake or ball.
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