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A bakery sells single layer mini-cakes that are 3 inches in diameter for $4 each. They also have a 9-inch cake for $15. If both cakes are the same thickness, which option gives you more cake for the money, nine mini-cakes or one 9-inch cake?

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SHARYNNE M. | Learning Made SimpleLearning Made Simple
4.9 4.9 (119 lesson ratings) (119)
Both cakes having the same thickness means both radius are the same.
-Solve for radius using diameter equation
-Use radius to find Circumference of each size cake
-Able to determine which cake size (mini-cakes, or bigger one) has larger circumference =the cake that gives you more value for the money
1. Diameter=  (2)(radius)
         3 inches=2r
         r=3/2 inch
2. Circumference= (pi)(diameter)
          =9.42 inches
3.  9.42 inches per 1 mini-cake
4. $4/cake(9 cakes)= $36
Option 1: You would get 84.78 inches of cake if you purchased 9 mini-cakes at $36
Big Cake: 
1. r=3/2 inches
2.  Circumference
         =3.14(9 inches)
         =28.26 inches
Option2: You would get 28.26 inches of cake if purchased 1 9-inch cake at $15
Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
The cakes are cylindrical.
Find the volume of each cake.
V=7.065h cubic units
V=63.585h cubic units
9 mini cakes costs $36 and you get 9*7.065h=63.585h cubic units of cake
1 large cake costs $15 and you get 63.585h cubic units of cake, the same amount !!!
the best buy is the 9-inch cake for only $15