Carcass wrote:
If the ratio of the surface areas of the two similar cubes in the figure below is 9:25, and if the volume of the smaller cube is 54, what is the volume of the larger cube?
Attachment:
GRe If the ratio of the surface areas of the two similar cubes.jpg
(A) 125
(B) 250
(C) 375
(D) 500
(E) 750
Surface area of a cube is 6a^, where a is side
Ratio of 2 sq is a^2/b^2 = 9/25, solving we get a/b =3/5. So side of smaller sq is multiple of 3 and bigger 5.
Volume of cube is a^, so post inputting given volume we can see it's 2 * 3^3, hence volume of bigger cube must be 2* 5^3 = 250
Ans is B
We could have tried b as 25 and calculate volume as 2 * 25^3 and it will be a very huge no. and all options are smaller.