Question 1203353
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When professional  Math writers formulate  Math problems in  English, 
they  NEVER  use the form  " 10 times taller ",  because such form is ambiguous in  English.


The standard form to use in  Math problems in  English for such situations 
is  " 10 times as tall as . . . ".



        The strict formal meaning of the form  " 10 times taller than . . . " 
        in  English is  " 11 times as tall as . . . ".


        You will be very surprised,  but it is so,  to great distinction from other languages,

        as well as from your native language.



To learn more,  read from this link


https://english.stackexchange.com/questions/221323/has-the-illogical-three-times-bigger-replaced-three-times-as-big-in-common-u



This error that you make in your post is a standard/typical mistake for newcomers:
they  ALL  do this mistake,  until somebody will disclose them the truth.



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As for the solution, below it is presented in short form.


<pre>
If "r" is the radius of the base of a cone and "h" is the cone's height,
then the volume of a cone is

    {{{V[cone]}}} = {{{(1/3)*pi*r^2*h}}}.


From the problem, we are given that 

    {{{V[cone]}}} = {{{(1/3)*pi*r^2*h}}} = 60  cm^3.


It implies that

    {{{pi*r^2*h}}} = 3*60  = 180 cm^3.


This formula says that the volume of a cylinder with the same base and the same height is 180 cm^3.


But since our cylinder is 10 times as tall as the cone, we should take 180 cm^3 ten times, which gives us the


<U>ANSWER</U>.  The volume of the cylinder under the problem's question is 1800 cm^3.
</pre>

Solved.