Question

MEDAL!!!!
If the scale factor of two similar solids of 5:13 what is the ratio of their corresponding areas and volumes?
A. 125:2,197 and 25:169
B. 25:169 and 125:2,197
C.10:26 and 15:39
D. 5:169 and 5:2,197

Answer 1

Let me show the relationship with a object measure 2.

In 1 dimension, the length is 2 units. That is all it has and is.

In 2 dimensions, it is area of 4 units\(^2\). The square on the units is important.

In 3 dimensions, it is volume of 8 units\(^3\). See how this is cubed now?

Do you see the relationship between length, area, and volume now? You can apply that to the ratio.

Answer 2

@e.mccormick i don't totally understand? Mind explaining a bit more?

Answer 3

In my simplified example:

\(\Large2^1\text{ means units}^1\)
\(\Large2^2\text{ means units}^2\)
\(\Large2^3\text{ means units}^3\)