a cake mix suggests the use of two 9 inch circular pans for a layer cake or one 13 inch by 9 inch rectangular pan

Question

a cake mix suggests the use of two 9 inch circular pans for a layer cake or one 13 inch by 9 inch rectangular pan for a sheet cake. if the sheet cake is about 2 inches high, how high would you expect each circular cake to be?

Answer 1

For the same amount of cake?

 

Let h be the height of one of the circular cake pans which would yield the same amount of cake as one rectangular pan.

 

The amount of cake from the sheet cake is 13 × 9 × 2 = 234 in³. This is the volume of cake made.

 

The amount of cake made from two circular pans would be 2π(9/2)²h, since 9/2 is the radius of each pan.

 

Set these equal to each other and solve for h:

 

234 = 2π(4.5)²h = 40.5π h = 127.23h

 

h = 234/127.23 = 1.83 inches high.

 

Without the frosting, the layer cake would have height 2(1.83) = 3.69 inches. The frosting would add more height, but you did not say anything about that in your problem.