Answer to Question #29967 in Analytic Geometry for Mary

Question

Find the reduced ratio of the volume of two cubes whose total areas are 8 and 18 respectively

Answer 1

Ratio of edges is k=a1/a2.
Ratio of surfaces is S1/S2=k^2=(a1/a2)^2
Ratio of Volumes is V1/V2=k^3=(a1/a2)^3

Suppose, that the first cube has edge A, and the second one - B, then according to mentioned above facts and using given data we have:

S1/S2=(A/B)^2=8/18=4/9
Taking square root we obtain: A/B=2/3.

Thus according to mentioned above facts and using found data we have:

Ratio of the volumes is V1/V2=(A/B)^3=8/27 - and that's the answer.