While Erica and Ken are exploring a cave, they each find a gold nugget shaped like a potato. When they take their nuggets to the metallurgist to be analyzed, they learn that Ken’s nugget weighs $5.6$ grams and the surface area of his nugget is $20$ cm$^2$. Erica’s nugget weighs $700$ grams and the surface area of Erica’s nugget is $500$ cm$^2$.

1. Are the two nuggets similar solids? Explain.

   Hint (a):

   Mass compares to volume.

2. If the gold nuggets are similar solids, what is the ratio of their lengths?

   Hint (b):

   If the ratio of the masses is $5.6/700$, what is the scale factor?