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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.

The diagram shows a cone of radius 16 cm. The curved surface area of the cone is 544π cm². Find the slant height, l, of the cone.

Learn how to find the slant height of a cone with a radius of 16 cm and a curved surface area of 544π cm². This problem demonstrates the application of the curved surface area formula of a cone, suitable for students in Grades 9-10.

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