a By dividing the length of two corresponding sides in the nuggets, we can obtain the linear scale factor between them. We know that the bigger nugget has a side that is 5 times as long as the corresponding side in the small nugget.
Side in big nugget/Corresponding side in small nugget=5
If we know the surface area and volume of the smaller nugget, by squaring and cubing the linear scale factor we can find the surface area and volume of the big nugget by multiplying the smaller nugget's values by these ratios.
A_(Erica)=A_(Ken)(5)^2 & ⇔ A_(Erica)=25A_(Ken)
V_(Erica)=V_(Ken)(5)^3 & ⇔ V_(Erica)=125V_(Ken)
This way we only have to pay for analyzing the small nugget. Note that this completely hinges on the fact that the nuggets are similar.
b From Part A we know that the area scale factor between the nuggets is 25. By substituting A_(Ken)= 20 into the formula we established in Part A, we can find the surface area of Erica's nugget.
A_(Erica)=25( 20) ⇔ A_(Erica)=500 cm^2
c From Part A we know that the volume scale factor between the nuggets is 125. By substituting V_(Ken)= 5.6 into the formula we established in Part A, we can find the weight of Erica's nugget.
