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 can't find the answer and therefor I can't explain to my step kids how it's done. I have been out of school to long!!
Assuming that all servings contain an equal measure of all parts, you can average the calories accross the pieces.
Volume of a cylinder: V = πr²H
r = 1/2d = 9 3/8 = 75/8 in.
H = 2(3.5) + 5/8 = 7 5/8 in. = 61/8 in.
Total volume of the cake: π(75/8)²(61/8) = 2105.388631 in³
Volume of chocolate frosting: V = π(9)²(1/4) = 63.61725124 in³
Volume of buttercream frosting: We'll need three cylinders for this one.
V of top = π(9)²(3/8) = 95.42587685 in³
V of sides = [ π(75/8)²(61/8) ] - [π(9)²(61/8) ] = 165.0624687 in³
total V of b. frosting: 260.4883456 in³
Volume of cake portion = 2[ π(9)²(3.5) ] = 1781.283035 in³
Calories from cake: 1781.283035 * 140 = 249379.6248 cal
Calories from chocolate frosting: 63.61725124 * 320 = 20357.5204 cal
Calories from buttercream: 260.4883456 * 470 = 122429.5224
Total calories in cake: 392166.6676 cal
Number of 800-calorie servings = 392166.6676/800 = 490, with a little less than a fourth left over.
All that talk of cake is making me hungry...
El que pega primero pega dos veces.
I think you could occupy a whole lesson with that one.
And they better serve cake afterwards.
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman