Help on homework!

Question

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?

Answer 1

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

 

Mini-Cakes:

 

1. Diameter=  (2)(radius)

         3 inches=2r

         r=3/2 inch

2. Circumference= (pi)(diameter)

          =3.14(3inches)

          =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

 

     

 

Answer 2

The cakes are cylindrical.

Find the volume of each cake.

V=pi*r²*h

V=3.14*(1.5)²*h

V=3.14*2.25*h

V=7.065h cubic units

 

V=pi*r²*h

V=3.14*(4.5)²*h

V=3.14*20.25*h

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