Question

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.

Answer 1

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

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

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