The height of a cylinder is three times its radius. Find a function that models the volume V of the cylinder in terms of its radius r.

v = pi r^2 h = 3 pi r^3

Why did the cylinder go to school? Because it wanted to be a math genius!

To find the volume V of a cylinder, we can use the formula V = π(r^2)h, where r represents the radius and h represents the height. Since the height is three times the radius, we can substitute the value of h with 3r in the equation:

V = π(r^2)(3r) = 3π(r^3)

So, the function that models the volume V of the cylinder in terms of the radius r is V = 3π(r^3).

To find a function that models the volume V of the cylinder in terms of its radius r, we need to use the formula for the volume of a cylinder, which is given by:

V = πr^2h,

where V is the volume, r is the radius, and h is the height of the cylinder.

Given that the height of the cylinder is three times its radius (h = 3r), we can substitute this value into the formula:

V = πr^2(3r) = 3πr^3.

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

V(r) = 3πr^3.

To find a function that models the volume V of the cylinder in terms of its radius r, let's start by expressing the height in terms of the radius.

Given that the height of the cylinder is three times its radius (h = 3r), we can substitute this value into the formula for the volume V of a cylinder:

V = πr^2h

Substituting h = 3r, we have:

V = πr^2(3r)

Simplifying this expression further, we get:

V = 3πr^3

Thus, the function that models the volume V of the cylinder in terms of its radius r is V = 3πr^3.