Question 73751
2)         The volume of a cylinder (think about the volume of a can) is given by V = {{{pi*r^2h}}} where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters.


a)
{{{V/(pi*r^2) = cross(pi)*cross(r^2)h/(cross(pi*r^2)) }}}To solve for h divide both sides by {{{pi*r^2}}} 
So h equals
{{{h=V/(pi*r^2)}}}
Since its a 100 cubic centimeter can h equals
{{{h=100/(pi*r^2)}}}



b)To find out the height if the radius is 2 cm, just plug in 2 for r for the 100 cubic centimeter can (this is given above)
{{{h=100/(pi*(2)^2)}}}Let r=2,V=100
{{{h=100/(4*pi)}}}
{{{h=25/(pi)}}}
{{{h=7.957747}}}Approximately
So the height is about 8 cm (rounded of course)



c)
To graph this function, let r be x and h be y.
{{{graph( 300, 200, -6, 5, -10, 20, 100/(3.14*x^2) )}}} Graph of {{{y=100/(pi*r^2)}}}