### Video Transcript

A right circular cone has a radius
of three π₯ plus six and its height is three units less than its radius. Express the volume of the cone as a
polynomial function, knowing that the volume of a cone with radius π and height β
is π equals one third ππ squared β.

So weβre told us that the radius
was three π₯ plus six and our height is three less than the radius, which we can
simplify. So β is equal to three π₯ plus
three. So if the volume is equal to
one-third ππ squared β, we can plug in three π₯ plus six for π and three π₯ plus
three for β.

Now since we have a one-third, that
can cancel with the threes for the height, and this will make our work a little bit
easier. So now we need to square three π₯
plus six, which is three π₯ plus six times three π₯ plus six. And now we need a foil. And when foiling that, it gives us
nine π₯ squared plus 18π₯ plus 18π₯ plus 36. So letβs simplify that before we
multiply by π₯ plus one. And we get π times nine π₯ squared
plus 36π₯ plus 36 times π₯ plus one. Now letβs distribute.

Distributing the nine π₯ squared to
π₯ plus one, we get nine π₯ cubed plus nine π₯ squared. Distributing the 36π₯ to π₯ plus
one, we get 36π₯ squared plus 36π₯. And distributing the 36 to the π₯
plus one, we get 36π₯ plus 36. Now we can combine like terms. Therefore, the volume is equal to
π times nine π₯ cubed plus 45π₯ squared plus 72π₯ plus 36.