Question

Two cubes have volumes in the ratio 1 : 27 then the ratio of the area of the face of one to that of the other is

• A. 1 : 3
• B. 1 : 6
• C. 1 : 9
• D. 1 : 18

Answer 1

The correct option is C 1 : 9

Let the of both cubes sides are s and S

Then volume of each cube are $s^3$ and $S^3$

And Then face area are $6s^2$and $6S^2$

But the volume of cube in ratio 1:27

Then $S^3=27s^3\Rightarrow S=3$

Face area of Cube one =6S=$6\times 3s=18s$

And face area second cube =6s

Then ratio of face area =$\frac{18s}{6s}=1:9$