The height of a cylinder is nine times its radius. Find a function that models the volume $$ V $$ of the cylinder in terms of its radius $$ r $$. $$ V(r)=\square $$ SUBMIT ANSWER

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To find the volume $$ V $$ of a cylinder in terms of its radius $$ r $$, we can use the formula for the volume of a cylinder:

$$
V = \pi r^2 h
$$

where $$ r $$ is the radius and $$ h $$ is the height of the cylinder.

According to the problem, the height $$ h $$ is nine times the radius $$ r $$. Therefore, we can express the height as:

$$
h = 9r
$$

Now, we can substitute this expression for $$ h $$ into the volume formula:

$$
V = \pi r^2 (9r)
$$

Now, we simplify this expression:

$$
V = 9\pi r^3
$$

Thus, the function that models the volume $$ V $$ of the cylinder in terms of its radius $$ r $$ is:

$$
V(r) = 9\pi r^3
$$

So, the final answer is:

$$
V(r) = 9\pi r^3
$$
$$ V(r) = 9\pi r^3 $$

The height of a cylinder is nine times its radius. Find a function that models the volume \( V \) of the cylinder in terms of its radius \( r \). \( V(r)=\square \) SUBMIT ANSWER

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