Question

the volume of 2 similar pyramid are in the ratio of 216:27 . what is the ratio of their a)height, b) diagonal?

Answer 1

volume of similar shapes is proportional to the cubes of their sides

so we need
ratio of their sides = 216^(1/3) : 27^(1/3)
= 6: 3
= 2 : 1

we could have seen that right away, since 216 : 27 = 8 : 1

since both height and diagonal are linear measurements, both of
these have that ratio
that is:
height of larger : height of smaller = 2 : 1
etc