Question 1210537
.
The curve surface area of a cylinder is 1.5 times the total surface area of a cone. 
If the diameter of the cylinder and cone are equal to 10cm and the vertical height of the cone is 12cm. 
Calculate the height of the cylinder
~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The curve surface area of this cylinder is  

    {{{A[cylinder]}}} = {{{2*pi*r*h}}} = {{{2pi*5*h}}} = {{{10*pi*h}}}.


The slant height of the cone is  

    L = {{{sqrt(12^2+5^2)}}} = {{{sqrt(144+25)}}} = {{{sqrt(169)}}} = 13 cm.


The total surface area of the cone is 

    {{{A[cone]}}} = {{{pi*r*L}}} + {{{pi*r^2}}} = {{{pi*5*13}}} + {{{pi*25}}} = {{{pi*(65+25)}}} = {{{90*pi}}}.


Now write the equation  {{{A[cylinder]}}} = {{{1.5*A[cone]}}}

    {{{10pi*h}}} = {{{1.5*90*pi}}}


Simplify it

     h = 1.5*9 =  13.5.


<U>ANSWER</U>.  The height of the cone is 13.5 cm.
</pre>

Solved.