Question 257144
the volumes of two similar solids, A and B, are in the ratio 1:64, respectively.
 What is the ratio of the surface area of solid A to the surface area of solid B? Express answer as a common fraction.
:
Use cubes for simplicity, with sides, x & y
{{{x^3/y^3}}} = {{{1/64}}}
y^3 = 64x^3
Cube root of both sides
y = 4x
:
Surface area
{{{(6x^2)/(6y^2)}}}
Cancel 6
{{{x^2/y^2}}}
Replace y with 4x
{{{x^2/((4x)^2)}}} = {{{x^2/(16x^2)}}} = {{{1/16}}}