Surface Area of A Cake

Question

A wedding cake has three tiers. Each tier is 10cm high. The layers have radii 22cm, 17cm and 12cm respectively. A pastry chef needs to determine the cost of the icing needed to decorate the cake. If the icing costs $3 per square centimetre, how much will it cost to decorate the entire cake (except for its base)?

Answer 1

Are these stacked directly on top of each as the 12 is on top of the 17 and the 17 is on top of the 22 or is there a stand/holder for each tier. If each cake had separate stand no icing would be needed on the bottom of each cake

I get the impression from the wording that the surface area of the 12 and 17 cm tiers are completely covered and the base of the 22 cm is the only part that is not covered. With that said, I'm assuming below that the cakes are stacked directly on top of each other 12 cm is on top of the 17 cm is on top of the 22 cm which is on the bottom; since the description does not mention any separation between the tiers. I do apologize for the long note.

Consider that a typical cake is in the shape of a cylinder. The height for each of your cylinders is 10 cm

The Surface area of a cylinder is

2πr² + 2πrh

The radius for each tier is given 12 cm, 17, and 22 cm

You have 3 cylinders stacked the 12 cm top tier, 17 cm middle tier, 22 cm as the bottom tier

You will need the surface area of 12 cm and 17 cm cylinder tiers

You will need the surface area of the 22 cm as πr² + 2πrh since you don't cover the base(the bottom of the last tier).

Calculate each surface area, add them together then multiply by $3 per square cm to get cost.

Give it a try