Question 211692
Brace yourself. This will be a bloody problem.
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First hand, you should know the formula for the surface area of a cylinder which is SA=2*pi*r<sup>2</sup> + 2*pi*r*h
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We are given the value SA=60. So...
{{{60=2*pi*r^2 + 2*pi*r*h}}}
Factoring {{{2*pi}}} out,
{{{60=2*pi*(r^2 + r*h)}}}
Dividing both sides by {{{2*pi}}},
{{{60/(2*pi)=r^2 + r*h}}}
{{{30/pi=r^2 + r*h}}}
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We now subtract {{{r^2}}} to both sides of the equation.
{{{30/pi-r^2 = r*h}}}
Then, we divide both sides by r.
{{{h=(30/pi-r^2)/r}}}
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Then, we use the formula for volume {{{V=pi*r^2*h}}}
So
{{{V=pi*r^2*((30/pi-r^2)/r)}}}
Then
{{{V=pi*r*(30/pi-r^2)}}}
Then
{{{V=r*(30-pi*r^2)}}}
And so,
{{{V=30r-pi*r^3}}}
That's it.