Question

If the volume of two cubes are in ratio of 27:64, then the ratio of their total surface area is

Answer 1

a is the length of one side of 1st cube.
b is the length of 2nd cube.
then,a^3/b^3=27/64
taking the cube root on both sides,we get
a/b=3/4
ie,a=3b/4
surface area of 1stcube/surface area of 2nd cube=6a^2/6b^2
=a^2/b^2
=(3b/4)^2/b^2
=9/16
=9:16