SOLUTION: Hi, I need help with this problem: Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Hei

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Question 263328: Hi, I need help with this problem: Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Height = 3 cm Middle Layer: Radius= 6cm Height = 4 cm Bottom layer: Radius = 10cm Height= 5cm If each tub of frosting costs $6.99 and a each tub of frosting covers 120 cm^2 of cake, figure out how much money your sister will have to spend on frosting.
Answer by nerdybill(7384) (Show Source):
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Your older sister is getting married and to save money she is making her own cylinder shaped cake with three layers. Top layer: Radius= 3cm Height = 3 cm Middle Layer: Radius= 6cm Height = 4 cm Bottom layer: Radius = 10cm Height= 5cm If each tub of frosting costs $6.99 and a each tub of frosting covers 120 cm^2 of cake, figure out how much money your sister will have to spend on frosting
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Surface Area = Area of top +Area of the side
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Surface Area = (Area of top) + (perimeter of top)* height
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Surface Area = (pi r^2) + (2 pi r)* h
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Top layer:
Surface Area = (3.14*3^2) + (2*3.14*3)* 3
Surface Area = (3.14*9) + (6*3.14)* 3
Surface Area = 84.78 cm^2
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Middle layer:
Surface Area = (3.14*6^2) + (2*3.14*6)* 4
Surface Area = (3.14*36) + (12*3.14)* 4
Surface Area = 263.76 cm^2
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Bottom layer:
Surface Area = (3.14*10^2) + (2*3.14*10)* 5
Surface Area = (3.14*100) + (20*3.14)* 5
Surface Area = 628 cm^2
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Total area = 976.54 cm^2
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Deciding how many tubs:
976.54/120 = 8.14 tubs
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Since you can't buy a partial tub, you must buy the next whole number up:
9 tubs of frosting
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Total cost:
9 * 6.99 = $62.91