Answer:
The ratio of their edges is 2:1
Step-by-step explanation:
Notice, that they give us information about how the volume of two cubes compare (ratio 8 to 1). Recall that the volume of a cube of side (or edge) "L" is given by: [tex]Volume\,\,=\,\,L^3[/tex]
Let's assign the letter "E" to the edge of the largest cube, in which case, the volume of this larger cube can be written as: [tex]E^3[/tex]
Let;s assign the letter "e" to the edge of the smaller cube, in which case, the volume of it would be : [tex]e^3[/tex]
Let's now make the ratio of these volumes (larger cube over smaller cube) equal to 8:1
[tex]\frac{E^3}{e^3} =\frac{8}{1} =8[/tex]
Now, notice that the quotient on the left, can be written as the cube of the quotient of the edges (by using property of exponents), at the same time that we write "8" as the number "2" cubed:
[tex]\frac{E^3}{e^3} =8\\(\frac{E}{e} )^3=8\\(\frac{E}{e} )^3=2^3[/tex]
Now, applying the cubic root on both sides of the equation, we can solve for the ratio of the edges (E/e):
[tex](\frac{E}{e} )^3=2^3\\\frac{E}{e} = 2[/tex]
Therefore, the ratio of their edges is 2:1
