11. if the scale factor of two similar solids in 3 : 14, what is the ratio of their corresponding areas? what is the ratio of their corresponding volumes?

For this case we have the following scale factor:
 k = 3/14
 Therefore, for the relationship of areas we have:
 A1 / A2 = k ^ 2 = (3/14) ^ 2
 A1 / A2 = 9/196
 For the relation of volumes we have:
 V1 / V2 = k ^ 3 = (3/14) ^ 3
 V1 / V2 = 27/2744
 
 The ratio of their corresponding areas is:
 9: 196
 The ratio of their corresponding volumes is:
 27: 2744