The problem asks us to find the slant height $l$ of the cone, given the radius $r = 16 \, \text{cm}$ and the curved surface area $A = 544\pi \, \text{cm}^2$.

The formula for the curved surface area of a cone is:

$A = \pi r l$

We can substitute the values for $A$ and $r$ and solve for $l$:

$544\pi = \pi \times 16 \times l$

Now, divide both sides by $\pi$:

$544 = 16l$

Solve for $l$:

$l = \frac{544}{16} = 34 \, \text{cm}$

Thus, the slant height $l$ of the cone is 34 cm.

Would you like any more details or further explanation?

Here are five related questions:

1. What is the formula for the total surface area of a cone?
2. How do you calculate the volume of a cone?
3. Can you find the height of the cone using the Pythagorean theorem, given $l$ and $r$?
4. How would the curved surface area change if the radius were doubled?
5. What is the difference between slant height and perpendicular height?

Tip: Always ensure that the units are consistent when calculating areas, volumes, or other quantities.