Question 1118196
<br>
If the cake needs to feed 40 people instead of 8, then the volume must be 5 times the volume of the smaller cake.<br>
So part c is simple to answer: the ratio of the volumes of the two cakes is 5:1.<br>
(Note: "scale factor" is generally reserved for use as the ratio of measurements of length; "scale factor of volume" is nonstandard usage.)<br>
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.<br>
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.<br>
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.<br>
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.<br>
Okay I suppose if a couple of people are willing to settle for smaller pieces.