Question 1044254
.
these two cylinders are similar.
the ratio of their volumes is 8:27.
the height of cylinder A is 12cm.
find the height of cylinder B.
~~~~~~~~~~~~~~~~~~~~~~~~~~~


The condition does't say whether A is the larger or the smaller cylinder.
I will assume that A is the smaller cylinder.


<pre>
Since the cylinders are similar and since the ratio of their volumes is {{{8/27}}},
the ratio of their linear dimensions/measures is {{{root(3, 8/27)}}} = {{{2/3}}}  (similarity coefficient).

Next, since the height of the smaller cylinder is 12 cm, then the height of the larger cylinder is {{{12*(3/2)}}} = 18 cm.
</pre>