Question 1118196: 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 greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
If the cake needs to feed 40 people instead of 8, then the volume must be 5 times the volume of the smaller cake.
So part c is simple to answer: the ratio of the volumes of the two cakes is 5:1.
(Note: "scale factor" is generally reserved for use as the ratio of measurements of length; "scale factor of volume" is nonstandard usage.)
If the ratio of volumes is 5:1, then the scale factor (ratio of lengths) is the cube root of that, or (cube root of 5):1 -- to several decimal places, 1.709975947.
Then the length of each edge of the larger cake is 6*1.709975947 = 10.25985568 inches and the height of the larger cake is half of that, or 5.12992784 inches.
If you use the approximate scale factor of 1.7 given in the problem, then the length of an edge of the larger cake is 6*1.7 = 10.2 inches and the height is half of that, or 5.1 inches.
But if you use that scale factor to find the ratio of volumes, then the volume of the cake is only enough to feed 39.304 people.
Okay I suppose if a couple of people are willing to settle for smaller pieces.
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