SOLUTION: 3. You work for a catering company making cakes. The catering company must create a hexagonal cake for a tool company. Your company currently makes a small cake that is hexagonal

Question 1117668: 3.
You work for a catering company making cakes. The catering company must create a hexagonal cake for a tool company. Your company currently makes a small cake that is hexagonal and serves 8 people. The tool company wants one cake to serve 40 people. To feed that many the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake. Each edge of the small cake is 6 inches and the height of the cake is 3 inches.
a. What is the length of the edge of the larger cake?
b. What is the height of the large cake?
c. Your boss wants to know the scale factor of the volume of the cakes so that he can make sure you have enough materials to create the cake. What is the scale factor for the volume?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
your small cake has side lengths of 6 and a height of 3.

your large cake has sides lengths of 1.7 * 6 = 10.2 and a height of 1.7 * 3 = 5.1.

the volume of your small cake is the area of the hexagonal base * the height.

the area of of the hexagonal base of your small cake is equal to 3 * sqrt(3) / 2 * the length of each side squared.

that would be equal to 3 * sqrt(3) / 2 * 6^2 = 93.53074361 square inches.

the volume of your small cake would be equal to the area of the hexagonal base * the height.

that would be equal to 93.53074361 * 3 = 280.5922308 cubic inches.

the area of the hexagonal base of your large cake is equal to 3 * sqrt(3) / 2 * (6 * 1.7)^2 = 3 * sqrt(3) / 2 * 10.2^2 = 270.303849 square inches.

the volume of your large cake would be equal to 270.303849 * 3 * 1.7 = 270.303849 * 5.1 = 1378.54963 cubic inches.

the scale factor of the volume of the cakes would be the volume of the large cake divided by the volume of the small cake.

that would be 1378.54963 cubic inches / 280.5922308 cubic inches = 4.913.

that would be the same as the scale factor of the dimensions of the cake cubed, which is equal to 1.7^3 = 4.913.

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