Math CentralQuandaries & Queries


Question from johnathan, a student:

Each layer of a 3 layer cake is a cylinder with height 7.5 cm. The bottom layer has diameter 25 cm. The middle layer has diameter 22.5 cm. The top layer has diameter 20 cm. The surface of the cake is frosted. What area of the cake is frosted. I get 1695.56 but the answer in the book is 2081.3

Hi Johnathan,

I got the same answer as the book.

I see 6 parts to be frosted, threes shaded light brown in the diagram and three shaded dark brown.


Together the three light brown parts form a disk of diameter 25 cm. find its area.

The largest of the dark brown pieces has the area of a rectangle of height 7.5 cm and length the circumference of a circle of diameter 25 cm. What is the area of this rectangle?

Likewise you can calculate the areas of the other two dark brown pieces as the areas of rectangles.

Add the areas to find the total area to be frosted.

Enjoy the cake,

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