Answer:
The ratio of their surface areas would 1:9 and the ratio of their volumes would be 1:27
Explanation:
Given Info: The sides of two cubes are in ratio of 1:3. We can assign one square x and the other square 3x.
We know that the area of a square is its side squared, and that a cube has 6 sides. So thus if we assign one side of the cube x we can assume that surface area is 6x^2:
Surface Area of Cube #1= 6x^2
Surface Area of Cube #2= 6((3x)^2) = 6(9x^2) = 54x^2
Ratio of Surface Area: 6x^2 : 54x^2 = 6:54 = 1:9
Now for the volume we know that it is equivalent to one side cubed. So after assigning x to one cube, we can assume that volume would be x^3.
Volume of Cube #1= x^3
Volume of Cube #2= (3x)^3 = 27x^3
Ratio of Volume: x^3: 27x^3 = 1:27
Hope this helps!