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
`image` and,
the ratio of their volumes would be

`3^(3): 14^(3) = 27 : 2744`

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