Question 276252
the volumes of two similar solids, A and B, are in the ratio 64,respectively.
What is the ratio of the surface area of solid A to the surface area of solid B?
 Can you please express it in a common fraction?
:
Assume they are cubes
Let x = side of the smaller
Let y = side of the larger
:
{{{x^3/y^3}}} = {{{1/64}}}
cross multipl
{{{y^3 = 64x^3}}}
Find the cube root of both sides
y = 4x
:
Surface area ratio
{{{6x^2/(6y^2)}}}
Replace y with 4x
{{{6x^2/6(4x)^2}}}
Cancel the 6
{{{x^2/(4x)^2}}} = {{{x^2/(16x^2)}}}
cancel x^2
{{{1/16}}} is the surface area fraction