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Math Help - volume of ingrediants in a cake

  1. #1
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    Help please

    I Need to know this or i'll fail!!

    A large cake was baked. 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.

    I really need some help!!
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  2. #2
    Site Founder MathGuru's Avatar
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    Hint Help

    First you need to find the volume of each ingredient in one slice of cake this is made by cutting twice from the center to the circumference of the pie. The two cuts are "theta" degrees apart.

    Come up with a function for

    calories = f(theta)

    then set the left side equal to 800 and solve for theta.

    Then do 360/theta (if you work in degree) and get the number of slices
    Last edited by MathGuru; November 17th 2005 at 03:26 PM.
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  3. #3
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    Still confused..

    I'm a high schooler and I am very happy you replied but I have know idea what that means,But I'm really happy you replied
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  4. #4
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    Are ya still there??

    Its an extra credit question,and I need the credit if I'm going to pass my Math class.(Our teacher is giving us three 100's and I really need it)
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  5. #5
    Site Founder MathGuru's Avatar
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    Try to break the slice into all of its peices and figure out the individual volumes for layer 1 and layer 2 and chocolate and frosting.

    Then multiply each volume by its calori density (given)

    Then add up all of the peices and set them = to 800.

    should be in the form:

    800=f(theta)

    then divide 360 by theta and round down.
    Attached Thumbnails Attached Thumbnails volume of ingrediants in a cake-cake.jpg   volume of ingrediants in a cake-slice-break-down.jpg  
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  6. #6
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    Thanks!!!!

    Is this correct?

    The Answer is 480.
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  7. #7
    Site Founder MathGuru's Avatar
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    Talking

    I drew it free hand. Sorry it's so messy. I licked my fingers afterwards. mmmmmmm.
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  8. #8
    Site Founder MathGuru's Avatar
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    First of all show your work!

    How many slices of 800 calorie cake fit into this pie? Did you answer this question? 480 slices? I don't think so.
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  9. #9
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    Bye!

    Thanks again!!
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