Question 1209427
<pre>     
<font color="blue">
The height of a cylinder is equal to the length of its diameter.</font>  

{{{height}}}{{{""=""}}}{{{diameter}}}{{{""=""}}}{{{2*radius}}}

{{{h}}}{{{""=""}}}{{{2r}}}

<font color="blue">The curved surface area of the cylinder is 100cm squared.</font> 

{{{2*pi*r*h}}}{{{""=""}}}{{{2*pi*r*2r}}}{{{""=""}}}{{{4*pi*r^2=100}}}

<font color="blue">Calculate the height</font>

First calculate the radius r

{{{4*pi*r^2}}}{{{""=""}}}{{{100}}}
{{{r^2}}}{{{""=""}}}{{{25/pi}}}
{{{r}}}{{{""=""}}}{{{5/sqrt(pi)}}}

{{{h}}}{{{""=""}}}{{{2r}}}{{{""=""}}}{{{2(5/sqrt(pi))=10/sqrt(pi)}}}

h is approximately 5.641895835 cm. Round as you were told.

Edwin</pre>