Question

The ratio of the volume of two cubes is 125 to 64. What is the ratio of their surface areas?

Answer 1

the volume of a cube is defined by x^3 where x is the length of an edge
the surface area of a cube is the area of a face of the cube times the number of faces, so 6x^2

5^3=125 and 4^3=64

Answer 2

Volume of cube is given by; \(a^3\)

So find the ratio first:

\[\large \frac{a_1^3}{a_2^3} = \frac{125}{64} \implies \frac{a_1}{a_2} = \frac{5}{4}\]

Surface area of Cube is given by: \(\large 6a^2\)
Now take the ratio of surface area:

\[\large \frac{6a_1^2}{6a_2^2} = \frac{5^2}{4^2}\]

Square them you will have your ratio..
Tell me what do you get?

Answer 3

lol weird notations =))