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?

Question

Mathematics

Harrington

28 September, 08:10

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?

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Answers (1)

Know the Answer?

Roger Richards · Answer 1

a. What is the length of the edge of the larger cake?

10.2

b. What is the height of the large cake?

5.1

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?

4.913

Step-by-step explanation:

From the above question, we are given the following values

Small cake

It can feed 8 people

Length = 6

Height = 3

Large cake

Can feed 40 people

Length = unknown

Height = unknown

We are told from the question, that to feed 40 people, the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake

a. What is the length of the edge of the larger cake?

We are told from the question, that to feed 40 people, the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake

Hence, length of the large cake

= 1.7 * 6 = 10.2

b. What is the height of the large cake?

We are told from the question, that to feed 40 people, the length of each dimension of the larger cake will be about 1.7 times that of the smaller cake

Hence, height of the large cake

= 1.7 * 3 = 5.1

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?

From the above question, we can see that the dimension has been given already with is 1.7

When we are dealing with volume, scale factor represented by k is also always cubed.

Mathematically, when dealing volume, scale factor = k³

Where k = 1.7

Therefore, scale factor = 1.7³

= 4.913.