Two similar boxes have volumes of 250cm^3 and 54cm^3.what is the ratio of a)their heights
b)their surface areas?
for similar shapes or objects,
the volumes of similar objects are proportional to the cubes of their corresponding sides. So ...
height1^3 : height2^3 = 250 : 54 = 125 : 27
height1 : height2 = 125^(1/3) : 27^(1/3) = 5 : 3
the surface areas of similar objects are proportional to the squares of their corresponding sides, so ...
surface area1 : surface area2 = 5^2 : 3^2 = 25 : 9