Two similar boxes have volumes of 250cm^3 and 54cm^3.what is the ratio of a)their heights

b)their surface areas?

1 answer

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