Question 1011918
.
A cylinder is inscribed in a sphere of radius 1. Express the volume V of the cylinder as a function of the base radius r. 
----------------------------------------------------------------

<pre>
Volume of a cylinder is 

V = {{{pi*r^2*h}}},        (1)

where r is the radius of the cylinder and h is the height of the cylinder.

When cylinder of the radius r is inscribed in a sphere of radius r,

h = {{{2*sqrt(1-r^2)}}}       (2)

(make a sketch and apply the Pythagorean theorem).

Substitute (2) into (1), and you will get

V = {{{2*pi*r^2*sqrt(1-r^2)}}}.

This is the required formula.
</pre>


--------------------------------------------------------------------
<U>Comment from student</U>: Thanks. Please show me how you derive the height algebraically.
--------------------------------------------------------------------


<U>My responce</U>

<pre>

It is not algebraically.
It is geometrically.

Make a sketch of the section of the sphere with the cylinder inscribed.
Then apply the Pythagorean Theorem.

It is so obvious.
</pre>