Question 1011932
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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. 
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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.
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