### Home > CCG > Chapter 10 > Lesson 10.2.1 > Problem 10-69

“*I won’t have that kind of money until I sell my nugget, and then I won’t need it analyzed!”* Erica says.

“*Wait, Erica. Don’t worry. I’m pretty sure we can get all the information we need for only .”*

Explain how they can get all the information they need for

.Since the two nuggets are similar, if they spend

to get Ken's nugget analyzed, they can calculate the surface area and weight of Erica's nuggets using the ratios of similarity.

If Ken’s nugget has a surface area of

, what is the surface area of Erica’s nugget? We know the linear scale factor is

, so the ratio of the areas is , . If Ken’s nugget weighs

g (about oz), what is the weight of Erica’s nugget? Since the nuggets are solid gold and have the same density throughout, calculate the weight using the ratio of the volumes.