The volume of two similar solids are125 in ^3 and 216 in ^3. The surface area of the larger solid is 288 in^2. What is the surface area of the smaller solid?

Answer 1

The volumes of similar solids are proportional to the cube of their
corresponding sides
125 : 216 = s1^3 : s2^3
5^3 : 6^3 = s1^3 : s2^2
s1 : s2 = 5 : 6

the surface area of similar solids is proportional to the square of their
corresponding sides
a1 : a2 = 5^2 : 6^2 = 25 : 36

if a2 is the larger,
a1 : 288 = 25:36
a1 = 288(25)/36 = 200 <----- surface area of the smaller solid