Two cubes have their volumes in the ratio $$1:27$$. The ratio of their surface areas is
Correct option is B. $$1:9$$
Volumes are in the ratio $$1:27$$
Let the sides of the cubes are $$a,b$$. then
$$1/27=1/3=a^3/b^3$$
$$b/a=3$$
Since we know that the surface area of a cube is $$6a^2$$
$$i.e$$ the surface ares will be proportional to the square of sides.
Therefore on squaring $$\dfrac{a^2}{b^2}=\dfrac{1^2}{3^2}$$
$$=\dfrac{1}{9}=1:9$$