Asked by magdaline
the volume of 2 similar pyramid are in the ratio of 216:27 . what is the ratio of their a)height, b) diagonal?
Answers
Answered by
mathhelper
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
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