# Answer to Question #23219 in Geometry for Daryl Ligutan

Question #23219

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

Expert's answer

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)

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)

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