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A large birthday cake was baked to celebrate the 6th birthday of Mimi. 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.

  • Math -

    Total calories=140*cake volume+320Frosting volume.

    Frosting volume= volume middle+volume top+ volumesides.

    = PI*9^2*1/4 + PI*9^2*3/8 + (3.5+1/4+3.5+3/8)(PI*18)

    You find the volume of the cake, then proceed to find total calories, and divide that by 800.

  • Math -

    volume of vanilla cake = pi(9^2)(7)
    that answer times 140 gives vanilla calories.

    volume of chocolate frosting = pi(9^2)(.25)
    that times 320 gives you chocolate calories.

    frosting around the outside = pi(9.375^2)(7.25) - pi(9^2)(7.25)
    = icing-1

    for the top frosting
    = pi(9.375^2)(.375)
    = icing-2

    calories for frosting = 470(icing-1 + icing-2)

    add up all the calories.

    you do the math!

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