Question

1. A cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes.

Answer 1

Surface area of a cube S:
S = 6 a^2
a is the length of the side of each edge of the cube
Surface area of one face of a cube S1:
S1 = a'^2
a' is the length of the side
if S1 = S
6 a^2 = a'^2
a'/a = Sqrt[6]
Volume of a cube
V = a^3
Therefore
V'/V = (a'/a)^3 = 6^(3/2)
Answer: 6^(3/2)