Q:

If the similarity ratio of two similar solids is 3 : 14, what is the ratio of their corresponding areas? What is the ratio of their corresponding volumes? Question 22 options: The ratio of their corresponding areas is 27 : 2744. The ratio of their corresponding volumes is 9 : 196. The ratio of their corresponding areas is 3 : 196. The ratio of their corresponding volumes is 3 : 2744. The ratio of their corresponding areas is 6 : 28. The ratio of their corresponding volumes is 9 : 42. The ratio of their corresponding areas is 9 : 196. The ratio of their corresponding volumes is 27 : 2744.

Accepted Solution

A:
Note that, if the two solids are similar with a scale factor of x, then the ratio of their areas would be [tex] x^{2} [/tex] and the ratio of their volumes would be [tex] x^{3} [/tex]. 

In this case, the ratio of the two similar solids is 3:14. So the ratio of their areas would be [tex]
3^{2} : 14^{2} = 9 : 196 [/tex] and,
the ratio of their volumes would be
[tex] 3^{3}: 14^{3} = 27 : 2744 [/tex]

Thus, the answer is 9 : 196 and 27 : 2744.