"5 centimeters less than twice its radius" describes $h$ in terms of $r$. If "twice its radius" is $2r$, how do you write "5 less than" that quantity?

Substitute your expression for $h$ into the volume formula so that the only variable is $r$. Then simplify the left side and move everything to one side so the equation equals 0.

After you have something like $(\text{expression in } r) = 1{,}800$, think about what happens to the $1{,}800$ when you move it to the other side. Does it become $+1{,}800$ or $-1{,}800$ on the side with 0?

In Desmos, use $x$ instead of $r$. Enter the expression for the left side of the simplified volume equation as a function: type y = x^2(2x - 5).

Enter a second function for the constant volume: type y = 1800. The intersection points of these two graphs show values of $x$ that satisfy $x^2(2x - 5) = 1800$.

From the graph, you know the underlying equation before rearranging is $x^2(2x - 5) = 1800$. If you expand $x^2(2x - 5)$ and then move $1800$ to the same side as the $x$ terms so that the other side is 0, you will get a cubic expression. Choose the answer option whose equation matches that expanded and rearranged form (with $r$ in place of $x$).

For a right circular cylinder, the volume formula is $V = \pi r^2 h$.

We are told the volume is $1{,}800\pi$ cubic centimeters, so set up:

The problem says: "The cylinder’s height $h$ is 5 centimeters less than twice its radius $r$."

• "Twice its radius" means $2r$.
• "5 centimeters less than" that means you subtract 5 from $2r$.

So the relationship is: $h = 2r - 5$ (not $2r + 5$).

Replace $h$ in the volume equation with $2r - 5$:

Now divide both sides by $\pi$ (since $\pi \ne 0$):

Next, expand the left side:

So you have:

To get an equation equal to 0, subtract $1{,}800$ from both sides:

This is equivalent to

which matches choice D.