Yummy Conundrum

A large birthday cake was baked to celebrate the 6th birthday
of Neopets. It was a round cake, made of two layers of vanilla cake;
each layer was 18 inches in diameter and 3.5 inches tall. Between the
two layers was a quarter inch of chocolate frosting. And covering the
top and side of the cake was 3/8″ of buttercream frosting.

If the vanilla cake has 140 calories per cubic inch, and the
chocolate frosting has 320 calories per cubic inch, and the buttercream
frosting has 470 calories per cubic inch, how many 800-calorie servings
are in the cake? Please round down to the nearest serving.

Whip out your calculators for this one, and a piece of paper may come in handy! Click here to submit your answer.